Decomposition of L2L^{2}-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2} (\partial \Omega ; \mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $\mathbb{R}^d\setminus\partial \Omega$. Moreover, this decomposition is orthogonal if and only if $\partial \Omega$ is a sphere. We also show that any $f$ in $L^{2} (\partial \Omega ; \mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $\partial \Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $\partial \Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature

Unique reconstruction of simple magnetizations from their magnetic potential

Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of $L^{2}$-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in $L^2$ on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential

Robotic intra-row weed hoeing in maize and sugar beet

A prototype of robotic intra-row weed hoeing in maize and sugar beet is presented in this study. Weeds in the crop rows were identified using a bi-spectral image analysis system and shape analysis. Positions of weeds in the images were recorded. Selective weed control in the row was performed with a modified finger weeder driven by electrical motors. Speed of the finger weeder was increased at positions where only weeds were classified. The system was triggered by an encoder and controlled by a micro-controller. Roboter-gesteuerte Unkrauthacke in der Reihe von Mais und ZuckerrübenEin Prototyp einer roboter-gesteuerten Hacke zur Unkrautbekämpfung in den Reihen von Mais und Zuckerrübe wird in dieser Studie vorgestellt. Unkräuter und Kulturpflanzen wurden mit einer bi-spektralen Kamera und Formenanalyse erkannt. Die Positionen der Unkräuter im Bild wurden bestimmt. Die selektive Unkrautbekämpfung in der Reihe geschah mit einer modifizierten Fingerhacke, die über Elektromotoren angetrieben werden. Die Fingerhacke wurde beschleunigt, wenn nur Unkräuter in der Reihe klassifiziert wurden. Das System wurde mit einem Inkrementalgeber getriggert und über einen Micro-Controller gesteuert

Analysis of cilia dysfunction phenotypes in zebrafish embryos depleted of origin recognition complex factors

Meier–Gorlin syndrome (MGS) is a rare, congenital primordial microcephalic dwarfism disorder. MGS is caused by genetic variants of components of the origin recognition complex (ORC) consisting of ORC1–6 and the pre-replication complex, which together enable origin firing and hence genome replication. In addition, ORC1 has previously been shown to play a role in ciliogenesis. Here, we extend this work and investigate the function of ORC1 and two other members of the complex on cilia at an organismal level. Knockdown experiments in zebrafish confirmed the impact of ORC1 on cilia. ORC1-deficiency confers defects anticipated to arise from impaired cilia function such as formation of oedema, kidney cysts, curved bodies and left–right asymmetry defects. We found ORC1 furthermore required for cilium formation in zebrafish and demonstrate that ciliopathy phenotypes in ORC1-depleted zebrafish could not be rescued by reconstitution with ORC1 bearing a genetic variant previously identified in MGS patients. Loss-of-function of Orc4 and Orc6, respectively, conferred similar ciliopathy phenotypes and cilium shortening in zebrafish, suggesting that several, if not all, components of the ORC regulate ciliogenesis downstream to or in addition to their canonical function in replication initiation. This study presents the first in vivo evidence of an influence of the MGS genes of the ORC family on cilia, and consolidates the possibility that cilia dysfunction could contribute to the clinical manifestation of ORC-deficient MGS

Relation between composition and vacant oxygen sites in the mixed ionicelectronic conductors La5.4W1 yMyO12 delta M Mo, Re; 0 lt; y lt; 0.2 and their mother compound La6 xWO12 delta 0.4 lt; x lt; 0.8

A detailed analysis of specimen composition, water uptake and their interrelationship in the systems La6 xWO12 amp; 948; 0.4 amp; 8804; x amp; 8804;0.8 and La6 xW1 yMyO12 amp; 948; 0 amp; 8804;y amp; 8804;0.2; M Mo, Re is presented. The three specimen series were investigated in dry and wet D2O conditions. A systematic trend in mass loss and onset temperature variation was observed in La6 xWO12 amp; 948; 0.4 amp; 8804;x amp; 8804;0.8 . Even very small amounts lt; 1 wt of secondary phases were found to notably modify the specimen s water uptake and onset temperature of mass loss. The theoretical model for vacancy concentration available was used to calculate the vacant oxygen sites starting from mass loss values determined by thermogravimetry. A discrepancy between the calculated and observed concentration of vacant oxygen sites is observed for all three systems. The effect of substitution of W by Re or Mo on the vacancy amount is explained taking into account diffraction measurements and information on the oxidation state of the substituting elements Mo and R

Clinical effectiveness of online computerised cognitive-behavioural therapy without support for depression in primary care: randomised trial

BACKGROUND: Computerised cognitive-behavioural therapy (CCBT) might offer a solution to the current undertreatment of depression. AIMS: To determine the clinical effectiveness of online, unsupported CCBT for depression in primary care. METHOD: Three hundred and three people with depression were randomly allocated to one of three groups: Colour Your Life; treatment as usual (TAU) by a general practitioner; or Colour Your Life and TAU combined. Colour Your Life is an online, multimedia, interactive CCBT programme. No assistance was offered. We had a 6-month follow-up period. RESULTS: No significant differences in outcome between the three interventions were found in the intention-to-treat and per protocol analyses. CONCLUSIONS: Online, unsupported CCBT did not outperform usual care, and the combination of both did not have additional effects. Decrease in depressive symptoms in people with moderate to severe depression was moderate in all three interventions. Online CCBT without support is not beneficial for all individuals with depressio