Discrete Geometric Analysis

2004 ◽  
Keyword(s):  
Geometric Analysis ◽  
Discrete Geometric Analysis

Discrete Geometric Analysis

10.1142/e045 ◽  
2016 ◽  
Author(s):  
Martin T Barlow ◽  
Tibor Jordán ◽  
Andrzej Zuk
Keyword(s):  
Geometric Analysis ◽  
Discrete Geometric Analysis

scholarly journals Equivalence relations that act on bundles of hyperbolic spaces

2017 ◽  
Vol 38 (7) ◽  
pp. 2447-2492 ◽  
Author(s):  
LEWIS BOWEN
Keyword(s):  
Equivalence Relation ◽  
Metric Spaces ◽  
American Mathematical Society ◽  
Geometric Analysis ◽  
Hyperbolic Spaces ◽  
Mathematical Society ◽  
Equivalence Relations ◽  
Full Group ◽  
Different Types ◽  
Discrete Geometric Analysis

Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation. We classify elements of the full group according to their action on fields on boundary measures (extending earlier results of Kaimanovich [Boundary amenability of hyperbolic spaces.Discrete Geometric Analysis(Contemporary Mathematics, 347). American Mathematical Society, Providence, RI, 2004, pp. 83–111]), study the existence and residuality of different types of elements and obtain an analog of Tits’ alternative.

Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

1986 ◽  
Vol 44 ◽  
pp. 348-349
Author(s):  
D.F. Clapin ◽  
V.J.A. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Neurofibrillary Tangles ◽  
Liquid Crystalline ◽  
Amyloid Fibrils ◽  
Geometric Analysis ◽  
Paired Helical Filaments ◽  
Microscopic Level ◽  
Light Microscopic Level ◽  
Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

Geometric analysis

1976 ◽  
Vol 55 (2) ◽  
pp. 67
Author(s):  
C.A. Gladman ◽  
R.A. Williams
Keyword(s):  
Geometric Analysis

GEOMETRIC ANALYSIS OF CRUCIFORM AND TRIFORM SOLID PROPELLANT GRAINS

2001 ◽  
Vol 9 (ASAT CONFERENCE) ◽  
pp. 1-13
Author(s):  
ZAYED A-N.
Keyword(s):  
Solid Propellant ◽  
Geometric Analysis

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals Hip geometry in hip fracture patients in Greenland occurring over a 7.7-year period

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Inuuteq Fleischer ◽  
Mogens Laursen ◽  
Stig Andersen
Keyword(s):  
Hip Fracture ◽  
Femoral Neck ◽  
Fracture Risk ◽  
Cortical Thickness ◽  
Geometric Analysis ◽  
Osteoporotic Fractures ◽  
Premature Death ◽  
Neck Length ◽  
Hip Geometry ◽  
Lesser Trochanter

Abstract Background Hip geometry influences hip fracture risk. Hip fractures are common, and they are associated with pain, disability, premature death and marked costs on society. Osteoporotic fractures are frequent in Arctic populations and increase with advancing age in this society with a steep rise in life expectancy. Greenland Inuit is a distinct ethnic group, and data on hip geometry is missing. We thus aimed to describe hip geometry in 7.7 years of consecutive hip fracture patients in Greenland. Methods We evaluated collodiaphysial angle, femoral neck length, the outer and inner diameter of the femur at 2 and 5 centimetres below the centre of the lesser trochanter and the cortical thickness from pelvic and hip radiographs in all patients operated in Greenland over 7.7 years. We included all 84 patients with one non-fractured hip visible for geometric analysis. Analyses were conducted in duplicate. Results We found a collodiaphysial angle of 134.8/132.6o in men/women (p = 0.06) and a femoral neck length of 38.0/33.9 mm in men/women (p = 0.001). Cortical thickness was affected by sex in the adjusted analysis (p < 0.001). Cortical thickness index at 5 cm below the centre of the lesser trochanter decreased with age (p = 0.026) and may be influenced by height (2 cm below the centre of the lesser trochanter, p = 0.053). Conclusion Our findings differed from European data and suggest a delicate balance in hip geometry in Arctic populations. Ethnic peculiarities influence the structure of the hip and may influence fracture risk. A focus on hip geometry and risk factors for osteoporotic fractures in Arctic populations is warranted.

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