Display; A Lie

Two original poems

Delineation of a quick clay zone at Smørgrav, Norway, with electromagnetic methods under geotechnical constraints

In many coastal areas of North America and Scandinavia, post-glacial clay sediments have emerged above sea level due to iso-static uplift. These clays are often destabilised by fresh water leaching and transformed to so-called quick clays as at the investigated area at Smørgrav, Norway. Slight mechanical disturbances of these materials may trigger landslides. Since the leaching increases the electrical resistivity of quick clay as compared to normal marine clay, the application of electromagnetic (EM) methods is of particular interest in the study of quick clay structures.

For the first time, single and joint inversions of direct-current resistivity (DCR), radiomagnetotelluric (RMT) and controlled-source audiomagnetotelluric (CSAMT) data were applied to delineate a zone of quick clay. The resulting 2-D models of electrical resistivity correlate excellently with previously published data from a ground conductivity metre and resistivity logs from two resistivity cone penetration tests (RCPT) into marine clay and quick clay. The RCPT log into the central part of the quick clay identifies the electrical resistivity of the quick clay structure to lie between 10 and 80 O m. In combination with the 2-D inversion models, it becomes possible to delineate the vertical and horizontal extent of the quick clay zone. As compared to the inversions of single data sets, the joint inversion model exhibits sharper resistivity contrasts and its resistivity values are more characteristic of the expected geology. In our preferred joint inversion model, there is a clear demarcation between dry soil, marine clay, quick clay and bedrock, which consists of alum shale and limestone.

Topology synthesis of three-legged spherical parallel manipulators employing Lie group theory

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.