In this note we propose a new way of constructing compact 7-manifolds with a closed G 2-structure. As a result we find a first example of a closed G 2-structure on S 3 × S 4. We also prove that any integral closed G 2-structure on a compact 7-manifold M 7 can be obtained by embedding M 7 to a universal space (W 3(80+8.C 3 8) , h). MSC: 53C10, 53C42 Key words: closed G 2-structures, submanifolds...

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Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G which encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighbourhood, by showing that it is the tree of cylinders of a JSJ splitting.

Teacher: Can you solve this problem? (Gives student paper with 4 – 1 8 written at the top.) Student: (Writes 3 8 as answer). Three-eighths. I subtracted 1 from 4, and then kept the denominator, 8, the same. Teacher: Suppose you had four large brownies and you ate one eighth of one brownie. How many brownies would you have left? Student: (Pauses, then draws four rectangles, partitions one of the...

We explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems. The abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors’ paper in Math. Models Methods Appl. Sci. 22 (8) (2012). We illustrate this strategy by considering problems set in smooth domains...

Supersonic shear imaging (SSI) is an ultrasound imaging modality that can provide insight into tissue mechanics by measuring shear wave propagation speed, a property that depends on tissue elasticity. SSI has previously been used to characterize the increase in Achilles tendon shear wave speed that occurs with loading, an effect attributable to the strain-stiffening behavior of the tissue. Howe...

The crawling wave experiment was developed to capture a shear wave induced moving interference pattern that is created by two harmonic vibration sources oscillating at different but almost the same frequencies. Using the vibration sonoelastography technique, the spectral variance image reveals a moving interference pattern. It has been shown that the speed of the moving interference pattern, i....

[1] A high resolution active source dataset recorded across the Southern Alps of New Zealand displays unusually strong S-wave phases, which show minimal shear wave splitting. A suite of methods was used to analyse the data to minimize the uncertainty in the anisotropy measurements. We use the Silver and Chan [1991] method, cross correlation of stacked data, and deconvolution in combination with...

In all media in which the elastic stiffness tensor and density vary in space, an implicit, frequency-dependent anisotropy is present, even if the medium is locally isotropic. This predicts a non-linear, frequency-dependent polarization of body waves, and explains shear-wave splitting in heterogeneous media. Examples are presented for compressional and shear waves in a medium in which the elasti...

Many pathological processes in tissues are recognized by morphological changes that reflect alterations of the soft tissue mechanical properties. Ultrasound shear-wave imaging can provide quantitative information about soft tissue mechanical properties, specifically the complex shear modulus. Advancing this field has the potential to bridge molecular, cellular, and tissue biology and to influen...