A special kind of three-periodic minimal surface has been studied, namely surfaces that are generated from disc-like-spanned skew polygons and that intersect themselves exclusively along straight lines. A new procedure for their derivation is introduced in this paper. Several properties of each such surface may be deduced from its generating polygon: the full symmetry group of the surface, its orientability, the symmetry group of the oriented surface, the pattern of self-intersections, the branch points of the surface, the symmetry and periodicity of the spatial subunits demarcated by the surface, and the Euler characteristics both of the surface and of the spatial subunits. The corresponding procedures are described and illustrated by examples.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1107/s0108767398007521 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
CPR related injuries of the chest wall: direct and indirect fractures.
Eur J Trauma Emerg Surg
January 2025
Department of Trauma and Orthopedic Surgery, University Hospital Erlangen, Friedrich-Alexander University Erlangen-Nürnberg (FAU), Erlangen, Germany.
Background: Rib and sternum fractures are common injuries associated with cardiopulmonary resuscitation (CPR). The fracture mechanism is either direct by application of force on sternum and anterior ribs or indirect by bending through compression of the thorax. The aim of this study was to determine morphologies of rib fractures after CPR and to reevaluate prior findings on fracture localisation, type and degree of dislocation.
View Article and Find Full Text PDFProbing Macromolecular Conformation in Restricted Geometry by PEF: Application to Hydrophobically Modified PAMAM Dendrimers Isolated Inside Surfactant Micelles.
J Phys Chem B
January 2025
Institute for Polymer Research, Waterloo Institute for Nanotechnology, Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
The conformation of a series of zero-generation polyamidoamine dendrimers end-labeled with four 1-pyrene-butyroyl, -hexanoyl, -octanoyl, -decanoyl, and -dodecanoyl derivatives, referred to as the PyCX-PAMAM-G0 samples with = 4, 6, 8, 10, and 12, respectively, was characterized in ,-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), and aqueous solutions of 50 mM sodium dodecyl sulfate (SDS) or 50 mM dodecyltrimethylammonium bromide (DTAB). The conformation of the PyCX-PAMAM-G0 samples was determined from the global model-free analysis (MFA) of the fluorescence decays, which yielded the average rate constant (⟨⟩) for pyrene excimer formation (PEF) between an excited and a ground-state pyrenyl labels, with ⟨⟩ being proportional to the local concentration ([Py]) of the pyrenyl labels within the macromolecular volume; ⟨⟩-vs-[Py] plots yielded straight lines passing through the origin in DMF and DMSO, demonstrating that the internal segments of the dendrimers obeyed Gaussian statistics in these two solvents. In aqueous surfactant solutions, the hydrophobic pyrenyl labels induced the interactions of the PyCX-PAMAM-G0 dendrimers with the SDS and DTAB micelles.
View Article and Find Full Text PDFPurpose: To clarify the femoral tunnel location for a virtual anterior cruciate ligament (ACL) graft to simulate the native ACL.
Methods: Three-dimensional (3D) computed tomography (CT) and magnetic resonance imaging (MRI) were obtained in 14 normal knees in full extension. Two types of virtual triple bundle ACL grafts (VACLG) were created.
Facialprofile determination using a novel face analyzer orthodontic mobile application.
J Orthod Sci
November 2024
Department of Orthodontics, SRM Kattankulathur Dental College, Chennai, Tamil Nadu, India.
Objectives: To find out the difference, the type of facial profile, and facial asymmetry between manual methods and mobile application, which is named the face analyzer orthodontic application. Facial profiles can be determined from the side of the face, categorized into three types: straight, convex, and concave profiles. Facial asymmetry refers to the imbalance between facial components concerning size, shape, and opposing positions of planes, lines, or points.
View Article and Find Full Text PDFFrom Straight Lines to Twists and Turns: Finding Patterns Between Socio-Economics and Unequal Health Outcomes in the Life Course.
Sociol Health Illn
January 2025
Department Public Health and Primary Care/Health Campus The Hague, Leiden University Medical Centre, The Hague, Netherlands.
Despite welfare state expansion in liberal democracies during the 20th century, health inequalities between socio-economic groups persist. Understanding individuals' lived experiences can inform policy for reducing unequal health outcomes in these lives. We build on Fundamental Cause Theory (FCT), which posits that low socio-economic status is the fundamental cause of health problems in (later) life.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!