On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix

The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integrals over eigenvalues of Hermitian supermatrices. All results are obtained with all Efetov-Wegner terms which were unknown before in such an explicit and compact representation.Comment: 23 pages, PACS: 02.30.Cj, 02.30.Fn, 02.30.Px, 05.30.Ch, 05.30.-d, 05.45.M

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

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Hilbert space for quantum mechanics on superspace

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed

Rangelands Vegetation Mapping at Species Composition Level Using the \u3cb\u3eSPiCla\u3c/b\u3e Method: \u3cb\u3eS\u3c/b\u3eDM Based \u3cb\u3ePi\u3c/b\u3exel \u3cb\u3eCla\u3c/b\u3essification and Fuzzy Accuracy. A New Approach of Map Making

Vegetation maps have been made since centuries. The vegetation cover was represented as homogeneous mapping units (polygons), representing different vegetation types, where each type consists a combination of different plant species (floristic composition). More recent, with the use of satellite imagery, the polygons have been replaced by pixels with similar content as the polygon maps. In both approaches, field-observations were linked to the mapping units (polygons or pixels) often resulting in a complex of different vegetation types per mapping unit. In our new approach field data (sample points) on presence and abundance of individual grass species are spatially extrapolated based on a set of environmental layers, using the species distribution modelling approach (SDM). When combined, each pixel will contain its own set of information about the vegetation structure and its floristic composition. This new methodology (SPiCla) results in a very accurate and detailed vegetation map at pixel level, allowing extraction of very detailed, accurate and easy to update spatial information on e.g., forage production and quality (palatability) for rangelands management. As no exact boundaries exist, but only gradients, we introduced fuzzy accuracy. The resolution mainly depends on the resolution of (or one of) the environmental layers used, scale of interest and workability. The methodology is generic and applicable to any other region in the world

Supervised exercise therapy for intermittent claudication in a community-based setting is as effective as clinic-based

ObjectiveThis cohort study was conducted to determine the effect on walking distances of supervised exercise therapy provided in a community-based setting.MethodsThe study included all consecutive patients presenting at the vascular outpatient clinic with intermittent claudication, diagnosed by a resting ankle brachial index <0.9, who had no previous peripheral vascular intervention for peripheral arterial disease, no major amputation, and sufficient command of the Dutch language. The exclusion criterion was the inability to walk the baseline treadmill test for a minimum of 10 m. The intervention was a supervised exercise therapy in a community-based setting. A progressive treadmill test at baseline and at 1, 3, and 6 months of follow-up measured initial claudication distance and absolute claudication distance. Changes were calculated using the mean percentages of change.ResultsFrom January through October 2005, 93 consecutive patients with claudication were eligible. Overall, 37 patients discontinued the supervised exercise therapy program. Eleven stopped because of intercurrent diseases, whereas for 10, supervised exercise therapy did not lead to adequate improvement and they underwent a vascular intervention. Three patients quit the program, stating that they were satisfied with the regained walking distance and did not require further supervised exercise therapy. Ten patients were not motivated sufficiently to continue the program, and in three patients, a lack of adequate insurance coverage was the reason for dropping out. Data for 56 patients were used and showed a mean percentage increase in initial claudication distance of 187% after 3 months and 240% after 6 months. The mean percentage of the absolute claudication distance increased 142% after 3 months and 191% after 6 months.ConclusionSupervised exercise therapy in a community-based setting is a promising approach to providing conservative treatment for patients with intermittent claudication

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

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Prevalence and incidence rate of hospital admissions related to medication between 2008 and 2013 in The Netherlands

PURPOSE: In 2009 a Dutch guideline was published containing recommendations to reduce Hospital Admissions Related to Medications (HARMs). This study aims to examine time-trends of HARMs and their potential preventability between 2008 and 2013 in The Netherlands. METHODS: A retrospective prevalence study was conducted using the Dutch PHARMO Database Network. A semi-automated pre-selection was used to make a crude identification of possible HARMs of which four samples were selected. These were independently assessed with respect to causality and potential preventability by a physician and pharmacist. The results were stratified by age into 18-64 years and 65 years and older. For these groups the net prevalences and incidence rates of HARMs and potentially preventable HARMs were calculated for the years 2008, 2009, 2011 and 2013. RESULTS: Four samples of 467 (2008), 447 (2009), 446 (2011) and 408 (2013) admissions were assessed. The net prevalence of HARMs in the 18-64 years group was approximately four times smaller compared to the older group with a mean prevalence of 2.7% (95% confidence interval [CI]:2.4%-3.0%) and 10.2% (95%CI: 9.7%-10.7%) respectively. The potential preventability was 25.1% (18.4%-31.8%) and 48.3% (95%CI: 44.8%-51.8%), respectively. The prevalence of HARMs in both groups did not change significantly between 2008 and 2013 with 2.4% (95%CI: 1.9%-3.0%) and 10.0% (95%CI: 9.0%-11.0%) in 2008 and 3.1% (2.7%-3.5%) and 10.4% (95%CI: 9.4%-11.4%) in 2013, respectively. CONCLUSION: Despite efforts to reduce HARMs, the prevalence did not decrease over time. Additional measures are therefore necessary, especially in the elderly population