Closed G2 forms and special metrics

170 p.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Public service employment and the public-private wage differential in British regions

Thomas, Dennis, Henley, Andrew, 'Public service employment and the public-private wage differential in British regions', Regional Studies (2001) 35(3) pp.229-240 RAE2008

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Assessment of the origin and stability of Nifedipine polymorph IV by differential scanning calorimetry (DSC)

Purpose. To examine the thermal transition(s) between different polymorphic forms of Nifedipine and to define experimental conditions that lead to the generation of polymorph IV. Methods. Experiments were performed using a DSC 823e (Mettler Toledo). Nifedipine exists in four polymorphic forms, as well as an amorphous state. Examination of Nifedipine was conducted using the following method(s): cycle 1: 25ºC to 190ºC, 190ºC to 25ºC (formation of amorphous Nifedipine); cycle 2: 25ºC to X (60,70,80...150ºC), X to 25ºC; cycle 3: 25ºC to 190ºC and holding isothermally for 5 min between cycles (heating/cooling rate of 10ºC/min). Results. The amorphous state Nifedipine can sustain heating up to 90ºC without significant changes in its composition. Cycle 2 of amorphous material heated up to 90ºC shows only the glass transition at ~44ºC. In cycle 3 of the same material, a glass transition has been recorded at ~44ºC, followed by two exotherms (~100 and ~115ºC (crystallisation of polymorph III and II, respectively) and an endotherm (169ºC (melting of polymorphs I/II)). Samples that have been heated to temperatures between 100ºC and 120ºC in the second cycle showed a glass transition at ~44ºC and an additional exotherm at ~95ºC (crystallisation of polymorph III) on cooling a exotherm was observed at ~40ºC (crystallisation of polymorph IV). The same material showed no glass transition in cycle 3 but an endotherm at around 62ºC (melting of polymorph IV) an exotherm (~98ºC) and an endotherm (169ºC) melting of polymorph I/II. Heating the sample to a temperatures greater than 130ºC in cycle two results in a glass transition at ~44ºC, and two exotherms at ~102 and 125ºC (crystallisation of polymorphs III and I, respectively). Conclusions. DSC data suggests that polymorph IV can only be produced from amorphous or polymorph III samples. The presence of polymorph I or II drives the conversion of the less stable polymorphic form IV into the most stable form, I. Although form IV of Nifedipine can easily be created, following defined experimental conditions, it may only coexist with amorphous or polymorph III states. When polymorphs I and II are present in the sample polymorph IV cannot be etected.

Differential osmoregulatory capabilities of common spiny mice (Acomys cahirinus) from adjacent microhabitats

The osmoregulatory function of common spiny mice Acomys cahirinus living on opposite slopes of the lower Nahal Oren ('Evolution Canyon') on mount Carmel, Israel, was investigated by increasing the salinity of the water source whilst maintaining a high-protein diet. The southern-facing slope (SFS) of this canyon differs from the northern-facing slope (NFS) as it receives considerably more solar radiation and consequently forms a more xeric, sparsely vegetated habitat. During the summer, mice living on the two opposite slopes significantly differed in their urine osmolality, which also increased significantly as dietary salinity increased. Offspring of wild-captured mice, born in captivity, and examined during the winter, continued to show a difference in osmoregulatory function depending on the slope of origin. However, they differed from wild-captured mice, as they did not respond to the increase in dietary salinity by increasing the concentration of their urine, but rather by increasing the volume of urine produced. This study shows that A. cahirinus occupying different microhabitats may exhibit differences in their ability to concentrate urine and thus in their ability to withstand xeric conditions. We suggest that they may also differ genetically, as offspring from the NFS and SFS retain physiological differences, but further studies will be needed to confirm this hypothesis.

Functional Forms and Educational Production Functions

Different Functional Forms Are Proposed and Applied in the Context of Educational Production Functions. Three Different Specifications - the Linerar, Logit and Inverse Power Transformation (Ipt) - Are Used to Explain First Grade Students' Results to a Mathematics Achievement Test. with Ipt Identified As the Best Functional Form to Explain the Data, the Assumption of Differential Impact of Explanatory Variables on Achievement Following the Status of the Student As a Low Or High Achiever Is Retained. Policy Implications of Such Result in Terms of School Interventions Are Discussed in the Paper.

Unfolded singularities of analytic differential equations

La thèse est composée d’un chapitre de préliminaires et de deux articles sur le sujet du déploiement de singularités d’équations différentielles ordinaires analytiques dans le plan complexe. L’article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity traite le problème de l’équivalence analytique de familles paramétriques de systèmes linéaires en dimension 2 qui déploient une singularité résonante générique de rang de Poincaré 1 dont la matrice principale est composée d’un seul bloc de Jordan. La question: quand deux telles familles sontelles équivalentes au moyen d’un changement analytique de coordonnées au voisinage d’une singularité? est complètement résolue et l’espace des modules des classes d’équivalence analytiques est décrit en termes d’un ensemble d’invariants formels et d’un invariant analytique, obtenu à partir de la trace de la monodromie. Des déploiements universels sont donnés pour toutes ces singularités. Dans l’article Confluence of singularities of non-linear differential equations via Borel–Laplace transformations on cherche des solutions bornées de systèmes paramétriques des équations non-linéaires de la variété centre de dimension 1 d’une singularité col-noeud déployée dans une famille de champs vectoriels complexes. En général, un système d’ÉDO analytiques avec une singularité double possède une unique solution formelle divergente au voisinage de la singularité, à laquelle on peut associer des vraies solutions sur certains secteurs dans le plan complexe en utilisant les transformations de Borel–Laplace. L’article montre comment généraliser cette méthode et déployer les solutions sectorielles. On construit des solutions de systèmes paramétriques, avec deux singularités régulières déployant une singularité irrégulière double, qui sont bornées sur des domaines «spirals» attachés aux deux points singuliers, et qui, à la limite, convergent vers une paire de solutions sectorielles couvrant un voisinage de la singularité confluente. La méthode apporte une description unifiée pour toutes les valeurs du paramètre.

Differential induction, isolation, physicochemical and molecular characterization of temperate phages of environmental Vibrio cholerae as evidence of phage mediated Horizontal Gene Transfer

The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.

Differential changes in transforming growth factor β isoform expression during postnatal cardiac growth

Transforming growth factor-β (TGF-β) is synthesised as an inactive precursor protein; this is cleaved to produce the mature peptide and a latency associated protein (LAP), which remains associated with the mature peptide until activation by LAP degradation. Isoform specific antibodies raised against the LAPs for TGF-β2and -β3were used to determine the myocardial levels of LAP (activatable TGF-β) and full length precursor (inactive TGF-β) forms during post-natal development in the rat. TGF-β2was present predominantly as the precursor in 2 day old myocardium. There was an age-dependent shift from precursor protein to LAP between 2 and 28 days. A corresponding increase in the level of mature (activatable) TGF-β2was found. TGF-β3was detected in significant quantities only as LAP. However, a four-fold increase in the expression of TGF-β3LAP was observed between 2 and 28 days. The substantial increases in activatable forms of TGF-β2and -β3that occur in myocardium during the first 28 days of life in the rat support a role for these proteins in post-natal cardiac development.

Physiological and morphological adaptations of herbaceous perennial legumes allow differential access to sources of varyingly soluble phosphate

The aim of this study was to investigate the capacity of three perennial legume species to access sources of varyingly soluble phosphorus (P) and their associated morphological and physiological adaptations. Two Australian native legumes with pasture potential (Cullen australasicum and Kennedia prostrata) and Medicago sativa cv. SARDI 10 were grown in sand under two P levels (6 and 40 µg P g−1) supplied as Ca(H2PO4)2·H2O (Ca-P, highly soluble, used in many fertilizers) or as one of three sparingly soluble forms: Ca10(OH)2(PO4)6 (apatite-P, found in relatively young soils; major constituent of rock phosphate), C6H6O24P6Na12 (inositol-P, the most common form of organic P in soil) and FePO4 (Fe-P, a poorly-available inorganic source of P). All species grew well with soluble P. When 6 µg P g−1 was supplied as sparingly soluble P, plant dry weight (DW) and P uptake were very low for C. australasicum and M. sativa (0.1–0.4 g DW) with the exception of M. sativa supplied with apatite-P (1.5 g). In contrast, K. prostrata grew well with inositol-P (1.0 g) and Fe-P (0.7 g), and even better with apatite-P (1.7 g), similar to that with Ca-P (1.9 g). Phosphorus uptake at 6 µg P g−1 was highly correlated with total root length, total rhizosphere carboxylate content and total rhizosphere acid phosphatase (EC 3.1.3.2) activity. These findings provide strong indications that there are opportunities to utilize local Australian legumes in low P pasture systems to access sparingly soluble soil P and increase perennial legume productivity, diversity and sustainability.

Crosstalk between oestrogen receptors and thyroid hormone receptor isoforms results in differential regulation of the preproenkephalin gene

Nuclear receptors are ligand-activated transcription factors, which have the potential to integrate internal metabolic events in an organism, with consequences for control of behaviour. Previous studies from this laboratory have shown that thyroid hormone receptor (TR) isoforms can inhibit oestrogen receptor (ER)alpha-mediated induction of preproenkephalin (PPE) gene expression in the hypothalamus. Also, thyroid hormone administration inhibits lordosis, a behaviour facilitated by PPE expression. We have examined the effect of multiple ligand-binding TR isoforms on the ER-mediated induction of the PPE gene in transient transfection assays in CV-1 cells. On a natural PPE gene promoter fragment containing two putative oestrogen response elements (EREs), both ER alpha and beta isoforms mediate a four to five-fold induction by oestrogen. Cotransfection of TR alpha 1 along with ER alpha inhibited the ER alpha transactivation of PPE by approximately 50%. However, cotransfection with either TR beta 1 or TR beta 2 expression plasmids produced no effect on the ER alpha or ER beta mediated induction of PPE. Therefore, under these experimental conditions, interactions with a single ER isoform are specific to an individual TR isoform. Transfection with a TR alpha 1 DNA-binding mutant could also inhibit ER alpha transactivation, suggesting that competition for binding on the ERE may not be the exclusive mechanism for inhibition. Data with the coactivator, SRC-1, suggested that coactivator squelching may participate in the inhibition. In dramatic contrast, when ER beta is cotransfected, TR alpha 1 stimulated ER beta-mediated transactivation of PPE by approximately eight-fold over control levels. This is the first study revealing specific interactions among nuclear receptor isoforms on a neuroendocrine promoter. These data also suggest that the combinatorics of ER and TR isoforms allow multiple forms of flexible gene regulations in the service of neuroendocrine integration.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Protein variation in blood-dwelling schistosome worms generated by differential splicing of micro-exon gene transcripts

Schistosoma mansoni is a well-adapted blood-dwelling parasitic helminth, persisting for decades in its human host despite being continually exposed to potential immune attack. Here, we describe in detail micro-exon genes (MEG) in S. mansoni, some present in multiple copies, which represent a novel molecular system for creating protein variation through the alternate splicing of short (<= 36 bp) symmetric exons organized in tandem. Analysis of three closely related copies of one MEG family allowed us to trace several evolutionary events and propose a mechanism for micro-exon generation and diversification. Microarray experiments show that the majority of MEGs are up-regulated in life cycle stages associated with establishment in the mammalian host after skin penetration. Sequencing of RT-PCR products allowed the description of several alternate splice forms of micro-exon genes, highlighting the potential use of these transcripts to generate a complex pool of protein variants. We obtained direct evidence for the existence of such pools by proteomic analysis of secretions from migrating schistosomula and mature eggs. Whole-mount in situ hybridization and immunolocalization showed that MEG transcripts and proteins were restricted to glands or epithelia exposed to the external environment. The ability of schistosomes to produce a complex pool of variant proteins aligns them with the other major groups of blood parasites, but using a completely different mechanism. We believe that our data open a new chapter in the study of immune evasion by schistosomes, and their ability to generate variant proteins could represent a significant obstacle to vaccine development.