On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems

this paper depends strongly on a theorem of Carleman-HartmanWintner. This theorem is only true in two dimensional domains. In fact a straightforward generalization to more than two dimensional domains cannot be true. A counterexample to the proof of [15]forthe three dimensional case can be found by using a special harmonic function due to Kellogg [12]. This function is shown in [2]. A direct counterexample can be found in [13]. 2 Main result on smooth domain

On the invertibility of mappings arising in 2D grid generation problems

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube

A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak

Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend both on the type of boundary conditions and the sharpness exponent of the peak.Comment: 12 pages, 1 figure, submitted to Math. Mech. Compl. Sy

Nazi Punks Folk Off: Leisure, Nationalism, Cultural Identity and the Consumption of Metal and Folk Music

Far-right activists have attempted to infiltrate and use popular music scenes to propagate their racialised ideologies. This paper explores attempts by the far right to co-opt two particular music scenes: black metal and English folk. Discourse tracing is used to explore online debates about boundaries, belonging and exclusion in the two scenes, and to compare such online debates with ethnographic work and previous research. It is argued that both scenes have differently resisted the far right through the policing of boundaries and communicative choices, but both scenes are compromised by their relationship to myths of whiteness and the instrumentality of the pop music industry

A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Gesundheit und Leistungsfähigkeit von Milchkühen im ökologischen Landbau interdisziplinär betrachtet – eine (Interventions-) Studie zu Stoffwechselstörungen und Eutererkrankungen unter Berücksichtigung von Grundfuttererzeugung, Fütterungsmanagement und Tierhaltung

Im Mittelpunkt des Projektes stand die Stoffwechsel- und Eutergesundheit von ökologisch gehaltenen Milchkühen im prä- und peripartalen Zeitraum sowie in den ersten 100 Laktationstagen und deren Beeinflussung durch die Futter- und Nährstoffversorgung und die Haltungsumwelt im umfassenden Sinn. In einer bundesweiten Feldstudie auf 106 ökologisch wirtschaftenden Milchviehbetrieben erfolgten Erhebungen mit dem Ziel einer Risikomodellierung zu Stoffwechsel- und Eutererkrankungen. Vor diesem Hintergrund wurden die Produktionssysteme von der Pflanzenzusammensetzung im Grünland und im Ackerfutter über die Grobfutterproduktion, Futterqualität und Rationsgestaltung, Haltungsumwelt bis hin zur Tiergesundheit und Milchqualität analysiert, um hier einzelbetriebliche Risikoeinschätzungen vorzunehmen, Optimierungspotenziale aufzuzeigen und Handlungsempfehlungen abzuleiten, die anschließend betriebsindividuell implementiert wurden. Die Effektivität des so geschaffenen präventiv orientierten Tiergesundheitsmanagements wurde anhand der Entwicklung ausgewählter Kennzahlen der Euter- und Stoffwechselgesundheit geprüft. Es konnte gezeigt werden, dass sich mit dieser Vorgehensweise auch unter Praxisbedingungen die Tiergesundheitssituation signifikant verbes-sern lässt. Die Feldstudie wurde mit experimentellen Untersuchungen ergänzt, die sich speziellen Fragen der Analyse von nXP in Grasprodukten, des Kraftfuttereinsatzes, der Wahl der geeigneten Rasse, dem Infektionsgeschehen, der Nutzung von Haltungstechniken im Fütterungsmanagement und der Verbesserung der Grasnarbe widmeten. Die im Projekt generierten, aufgrund ihrer Ableitung aus der Praxis widerspruchsarmen Erkenntnisse wurden über vielfältige Formen des Wissenstransfers an die Akteure in der Ökologischen Milchviehhaltung vermittelt. Ein Merkblatt zur Euter- und Stoffwechselgesundheit bei Biomilchkühen und ein modular aufgebautes Wissenstransferkonzept wurden erarbeitet, um die Projektergebnisse nachhaltig nutzen zu können

Increased peri-ductal collagen micro-organization may contribute to raised mammographic density

BACKGROUND: High mammographic density is a therapeutically modifiable risk factor for breast cancer. Although mammographic density is correlated with the relative abundance of collagen-rich fibroglandular tissue, the causative mechanisms, associated structural remodelling and mechanical consequences remain poorly defined. In this study we have developed a new collaborative bedside-to-bench workflow to determine the relationship between mammographic density, collagen abundance and alignment, tissue stiffness and the expression of extracellular matrix organising proteins. METHODS: Mammographic density was assessed in 22 post-menopausal women (aged 54–66 y). A radiologist and a pathologist identified and excised regions of elevated non-cancerous X-ray density prior to laboratory characterization. Collagen abundance was determined by both Masson’s trichrome and Picrosirius red staining (which enhances collagen birefringence when viewed under polarised light). The structural specificity of these collagen visualisation methods was determined by comparing the relative birefringence and ultrastructure (visualised by atomic force microscopy) of unaligned collagen I fibrils in reconstituted gels with the highly aligned collagen fibrils in rat tail tendon. Localised collagen fibril organisation and stiffness was also evaluated in tissue sections by atomic force microscopy/spectroscopy and the abundance of key extracellular proteins was assessed using mass spectrometry. RESULTS: Mammographic density was positively correlated with the abundance of aligned periductal fibrils rather than with the abundance of amorphous collagen. Compared with matched tissue resected from the breasts of low mammographic density patients, the highly birefringent tissue in mammographically dense breasts was both significantly stiffer and characterised by large (>80 μm long) fibrillar collagen bundles. Subsequent proteomic analyses not only confirmed the absence of collagen fibrosis in high mammographic density tissue, but additionally identified the up-regulation of periostin and collagen XVI (regulators of collagen fibril structure and architecture) as potential mediators of localised mechanical stiffness. CONCLUSIONS: These preliminary data suggest that remodelling, and hence stiffening, of the existing stromal collagen microarchitecture promotes high mammographic density within the breast. In turn, this aberrant mechanical environment may trigger neoplasia-associated mechanotransduction pathways within the epithelial cell population. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13058-015-0664-2) contains supplementary material, which is available to authorized users

Identification of phenotypic and transcriptomic signatures underpinning maize crown root systems

Maize is pivotal in supporting global agriculture and addressing food security challenges. Crop root systems are critical for water uptake and nutrient acquisition, which impacts yield. Quantitative trait phenotyping is essential to understand better the genetic factors underpinning maize root growth and development. Root systems are challenging to phenotype given their below-ground, soil-bound nature. In addition, manual trait annotations of root images are tedious and can lead to inaccuracies and inconsistencies between individuals, resulting in data discrepancies. In this study, we explored juvenile root phenotyping in the presence and absence of auxin treatment, a key phytohormone in root development, using manual curation and gene expression analyses. In addition, we developed an automated phenotyping pipeline for field-grown maize crown roots by leveraging open-source software. By examining a test set of 11 diverse maize genotypes for juvenile-adult root trait correlations and gene expression patterns, an inconsistent correlation was observed, underscoring the developmental plasticity prevalent during maize root morphogenesis. Transcripts involved in hormone signaling and stress responses were among differentially expressed genes in roots from 20 diverse maize genotypes, suggesting many molecular processes may underlie the observed phenotypic variance. In particular, co-expressed gene expression networks associated with module-trait relationships included 1,3-β-glucan, which plays a crucial role in cell wall dynamics. This study furthers our understanding of genotype-phenotype relationships, which is relevant for informing agricultural strategies to improve maize root physiology.This article is published as Callwood, Jodi B., Craig L. Cowling, Ella G. Townsend, Shikha Malik, Melissa A. Draves, Jasper Khor, Jackson P. Marshall, Heather Sweers, Justin W. Walley, and Dior R. Kelley. "Identification of phenotypic and transcriptomic signatures underpinning maize crown root systems." Plant Phenomics 7 (2025): 100008. doi:10.1016/j.plaphe.2025.100008