Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

The Early Days of Research on Carbonic Anhydrase

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73862/1/j.1749-6632.1984.tb12310.x.pd

Artificial drainage of peatlands: hydrological and hydrochemical process and wetland restoration

Peatlands have been subject to artificial drainage for centuries. This drainage has been in response to agricultural demand, forestry, horticultural and energy properties of peat and alleviation of flood risk. However, the are several environmental problems associated with drainage of peatlands. This paper describes the nature of these problems and examines the evidence for changes in hydrological and hydrochemical processes associated with these changes. Traditional black-box water balance approaches demonstrate little about wetland dynamics and therefore the science of catchment response to peat drainage is poorly understood. It is crucial that a more process-based approach be adopted within peatland ecosystems. The environmental problems associated with peat drainage have led, in part, to a recent reversal in attitudes to peatlands and we have seen a move towards wetland restoration. However, a detailed understanding of hydrological, hydrochemical and ecological process-interactions will be fundamental if we are to adequately restore degraded peatlands, preserve those that are still intact and understand the impacts of such management actions at the catchment scale

Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.Comment: 27 pages, LaTeX2e (IOP style

Mathematical practices and mathematical modes of enquiry: Same or different?

Background: In this paper, I share a case study of a teacher’s work on mathematics tasks in the context of a ‘mathematics for teaching’ course aiming to develop mathematical content understandings and mathematical practices among primary teachers in one South African province. The course was developed in a national context of concerns about the nature and levels of primary teachers’ mathematical knowledge. Theories viewing mathematical practices as fundamental, contrasted with those that view mathematical practices and mathematical content in more separate and ‘to be integrated’ ways, are used to frame the analysis and ritically reflect on the findings. Results: Data from this teacher’s pre-test and selected course assessments and interactions suggest that while he was able to develop some aspects of the mathematical practices described in the literature, his overall orientation remained attuned to memorization and recall. Findings also pointed to an ongoing reliance on external validation of the ‘correctness’ of his answers. Conclusions: The data suggest that the presence of elements of mathematical practices cannot be viewed as equivalent to the presence of mathematical modes of enquiry. The analysis presented in this paper suggests that while elements of mathematical practices can be developed, moving towards an encompassing orientation to mathematical modes of enquiry may require more central focus on problem-solving approaches to achieve a change in orientation

HIV-Specific T-Cells Accumulate in the Liver in HCV/HIV Co-Infection

BACKGROUND AND AIMS: Hepatitis C Virus (HCV)-related liver disease progresses more rapidly in individuals co-infected with Human Immunodeficiency Virus-1 (HIV), although the underlying immunologic mechanisms are unknown. We examined whether HIV-specific T-cells are identified in the liver of HCV/HIV co-infected individuals and promote liver inflammation through bystander immune responses. METHODS: Ex-vivo intra-hepatic lymphocytes from HCV mono-infected and HCV/HIV co-infected individuals were assessed for immune responses to HIV and HCV antigens by polychromatic flow cytometry. RESULTS: HCV/HIV liver biopsies had similar frequencies of lymphocytes but lower percentages of CD4+ T-cells compared to HCV biopsies. In co-infection, intra-hepatic HIV-specific CD8+ and CD4+ T-cells producing IFN-gamma and TNF-alpha were detected and were comparable in frequency to those that were HCV-specific. In co-infected individuals, viral-specific CD8+ T-cells produced more of the fibrogenic cytokine, TNF-alpha. In both mono- and co-infected individuals, intra-hepatic HCV-specific T-cells were poorly functional compared to HIV-specific T-cells. In co-infection, HAART was not associated with a reconstitution of intra-hepatic CD4+ T-cells and was associated with reduction in both HIV and HCV-specific intra-hepatic cytokine responses. CONCLUSION: The accumulation of functional HIV-specific T-cells in the liver during HCV/HIV co-infection may represent a bystander role for HIV in inducing faster progression of liver disease

Tortricid Moths Reared from the Invasive Weed Mexican Palo Verde, Parkinsonia aculeata, with Comments on their Host Specificity, Biology, Geographic Distribution, and Systematics

As part of efforts to identify native herbivores of Mexican palo verde, Parkinsonia aculeata L. (Leguminosae: Caesalpinioideae), as potential biological control agents against this invasive weed in Australia, ten species of Tortricidae (Lepidoptera) were reared from Guatemala, Mexico, Nicaragua, and Venezuela: Amorbia concavana (Zeller), Platynota rostrana (Walker), Platynota helianthes (Meyrick), Platynota stultana Walsingham (all Tortricinae: Sparganothini), Rudenia leguminana (Busck), Cochylis sp. (both Tortricinae: Cochylini), Ofatulena duodecemstriata (Walsingham), O. luminosa Heinrich, Ofatulena sp. (all Olethreutinae: Grapholitini), and Crocidosema lantana Busck (Olethreutinae: Eucosmini). Significant geographic range extensions are provided for O. duodecemstriata and R. leguminana. These are the first documented records of P. aculeata as a host plant for all but O. luminosa. The four species of Sparganothini are polyphagous; in contrast, the two Cochylini and three Grapholitini likely are specialists on Leguminosae. Ofatulena luminosa is possibly host specific on P. aculeata. Host trials with Rudenia leguminana also provide some evidence of specificity, in contrast to historical rearing records. To examine the possibility that R. leguminana is a complex of species, two data sets of molecular markers were examined: (1) a combined data set of two mitochondrial markers (a 781-basepair region of cytochrome c oxidase I (COI) and a 685-basepair region of cytochrome c oxidase II) and one nuclear marker (a 531-basepair region of the 28S domain 2); and (2) the 650-basepair “barcode” region of COI. Analyses of both data sets strongly suggest that individuals examined in this study belong to more than one species

Ecosystem services of temporary streams differ between wet and dry phases in regions with contrasting climates and economies

1. Temporary streams are dynamic ecosystems in which mosaics of flowing, ponded and dry habitats support high biodiversity of both aquatic and terrestrial species. Species interact within habitats to perform or facilitate processes that vary in response to changing habitat availability. A natural capital approach recognizes that, through such processes, the ‘natural assets’ of all ecosystems deliver services that benefit people. 2. The ecosystem services of temporary streams remain largely unexplored, in particular those provided during ponded and dry phases. In addition, recent characterizations have focused on dryland systems, and it remains unclear how service provision varies among different climatic regions, or between developed and developing economies. 3. We use evidence from interdisciplinary literature to examine the ecosystem services delivered by temporary streams, including the regulating, provisioning and cultural services provided across the continuum from flowing to dry conditions. We focus on service provision during dry phases and wet–dry transitions, across regions with contrasting climates and economic development. 4. Provision of individual services in temporary streams may be reduced, enhanced or changed by surface water loss. Services enhanced by dry phases include provision of higher‐quality subsurface drinking water and unique opportunities for recreation. Shifts between dry and wet phases enable groundwater recharge that mitigates water scarcity, and grant dry‐phase access to sediments deposited during flowing phases. However, the accessibility and thus perceived value of these and other services varies considerably among regions. In addition, accessing provisioning services requires careful management to promote sustainable resource use and avoid ecological degradation. 5. We highlight the need for environmental managers to recognize temporary streams as aquatic–terrestrial ecosystems, and to take actions promoting their diversity within functional socio‐ecological systems that deliver unique service bundles characterized by variability and differing availability in space and time