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

Biomass partitioning and root morphology of savanna trees across a water gradient.

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The effect of high dose inhaled corticosteroids on wheeze in infants after respiratory syncytial virus infection: randomised double blind placebo controlled trial

Objective To determine whether early initiated anti-inflammatory therapy with prolonged high dose inhaled glucocorticoids influences the occurrence and severity of recurrent wheeze after respiratory syncytial virus related lower respiratory tract infections

Methodological quality of a systematic review on physical therapy for temporomandibular disorders: influence of hand search and quality scales

The validity of a systematic review depends on completeness of identifying randomised clinical trials (RCTs) and the quality of the included RCTs. The aim of this study was to analyse the effects of hand search on the number of identified RCTs and of four quality lists on the outcome of quality assessment of RCTs evaluating the effect of physical therapy on temporomandibular disorders. In addition, we investigated the association between publication year and the methodological quality of these RCTs. Cochrane, Medline and Embase databases were searched electronically. The references of the included studies were checked for additional trials. Studies not electronically identified were labelled as “obtained by means of hand search”. The included RCTs (69) concerning physical therapy for temporomandibular disorders were assessed using four different quality lists: the Delphi list, the Jadad list, the Megens & Harris list and the Risk of Bias list. The association between the quality scores and the year of publication were calculated. After electronic database search, hand search resulted in an additional 17 RCTs (25%). The mean quality score of the RCTs, expressed as a percentage of the maximum score, was low to moderate and varied from 35.1% for the Delphi list to 54.3% for the Risk of Bias list. The agreement among the four quality assessment lists, calculated by the Interclass Correlation Coefficient, was 0.603 (95% CI, 0.389; 0.749). The Delphi list scored significantly lower than the other lists. The Risk of Bias list scored significantly higher than the Jadad list. A moderate association was found between year of publication and scores on the Delphi list (r = 0.50), the Jadad list (r = 0.33) and the Megens & Harris list (r = 0.43)

Invariant integration on orthosymplectic and unitary supergroups

The orthosymplectic supergroup OSp(m|2n) and unitary supergroup U(p|q) are studied following a new approach that starts from Harish-Chandra pairs and links the sheaf-theoretical supermanifold approach of Berezin and others with the differential geometry approach of Rogers and others. The matrix elements of the fundamental representation of the Lie supergroup G are expressed in terms of functions on the product supermanifold G_0 x R^{0|N}, with G_0 the underlying Lie group and N the odd dimension of G. This product supermanifold is isomorphic to the supermanifold of G. This leads to a new expression for the standard generators of the corresponding Lie superalgebra g as invariant derivations on G. Using these results a new and transparent formula for the invariant integrals on OSp(m|2n) and U(p|q) is obtained

Action research and democracy

This contribution explores the relationship between research and learning democracy. Action research is seen as being compatible with the orientation of educational and social work research towards social justice and democracy. Nevertheless, the history of action research is characterized by a tension between democracy and social engineering. In the social-engineering approach, action research is conceptualized as a process of innovation aimed at a specific Bildungsideal. In a democratic approach action research is seen as research based on cooperation between research and practice. However, the notion of democratic action research as opposed to social engineering action research needs to be theorized. So called democratic action research involving the implementation by the researcher of democracy as a model and as a preset goal, reduces cooperation and participation into instruments to reach this goal, and becomes a type of social engineering in itself. We argue that the relationship between action research and democracy is in the acknowledgment of the political dimension of participation: ‘a democratic relationship in which both sides exercise power and shared control over decision-making as well as interpretation’. This implies an open research design and methodology able to understand democracy as a learning process and an ongoing experiment

Liver-Specific Commd1 Knockout Mice Are Susceptible to Hepatic Copper Accumulation

Canine copper toxicosis is an autosomal recessive disorder characterized by hepatic copper accumulation resulting in liver fibrosis and eventually cirrhosis. We have identified COMMD1 as the gene underlying copper toxicosis in Bedlington terriers. Although recent studies suggest that COMMD1 regulates hepatic copper export via an interaction with the Wilson disease protein ATP7B, its importance in hepatic copper homeostasis is ill-defined. In this study, we aimed to assess the effect of Commd1 deficiency on hepatic copper metabolism in mice. Liver-specific Commd1 knockout mice (Commd1Δhep) were generated and fed either a standard or a copper-enriched diet. Copper homeostasis and liver function were determined in Commd1Δhep mice by biochemical and histological analyses, and compared to wild-type littermates. Commd1Δhep mice were viable and did not develop an overt phenotype. At six weeks, the liver copper contents was increased up to a 3-fold upon Commd1 deficiency, but declined with age to concentrations similar to those seen in controls. Interestingly, Commd1Δhep mice fed a copper-enriched diet progressively accumulated copper in the liver up to a 20-fold increase compared to controls. These copper levels did not result in significant induction of the copper-responsive genes metallothionein I and II, neither was there evidence of biochemical liver injury nor overt liver pathology. The biosynthesis of ceruloplasmin was clearly augmented with age in Commd1Δhep mice. Although COMMD1 expression is associated with changes in ATP7B protein stability, no clear correlation between Atp7b levels and copper accumulation in Commd1Δhep mice could be detected. Despite the absence of hepatocellular toxicity in Commd1Δhep mice, the changes in liver copper displayed several parallels with copper toxicosis in Bedlington terriers. Thus, these results provide the first genetic evidence for COMMD1 to play an essential role in hepatic copper homeostasis and present a valuable mouse model for further understanding of the molecular mechanisms underlying hepatic copper homeostasis