We show that every sheaf on the site of smooth manifolds with values in a stable
(
∞
,
1
)
-category (like spectra or chain complexes) gives rise to a “differential cohomology diagram” and a homotopy ...formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy invariant part and a piece which has a trivial evaluation on a point. In the classical examples the latter is the contribution of differential forms. This decomposition suggests a natural scheme to analyse new sheaves by determining these pieces and the gluing data. We perform this analysis for a variety of classical and not so classical examples.
The Ptolemy variety for
SL
(
2
,
C
)
is an invariant of a topological ideal triangulation of a compact 3-manifold
M
. It is closely related to Thurston’s gluing equation variety. The Ptolemy variety ...maps naturally to the set of conjugacy classes of boundary-unipotent
SL
(
2
,
C
)
-representations, but (like the gluing equation variety) it depends on the triangulation, and may miss several components of representations. In this paper, we define a Ptolemy variety, which is independent of the choice of triangulation, and detects all boundary-unipotent irreducible
SL
(
2
,
C
)
-representations. We also define variants of the Ptolemy variety for
PSL
(
2
,
C
)
-representations, and representations that are not necessarily boundary-unipotent. In particular, we obtain an algorithm to compute all irreducible
SL
(
2
,
C
)
-characters as well as the full
A
-polynomial. All the varieties are topological invariants of
M
.
Lidar is important active remote sensing equipment in the field of atmospheric environment detection. However, the detection range of lidar is severely limited by the dynamic range of photodetectors. ...To solve this problem, atmospheric lidars are often equipped with two or more channels to receive signals from different altitude ranges, where gluing the multi-channel echo signals becomes a key issue for accurate data inversion. In this paper, a multi-channel signal gluing algorithm based on the Improved Gray Wolf Optimizer (IGWO) and Neighborhood Rough Set (NRS), named IGWO-RSD, is proposed. The fitness function F is formed by three objective functions: correlation coefficient R, regression stability coefficient S and mean fit deviation D. All three objective functions are obtained from the data itself and do not rely on prior information. The weights of the objective functions R, S and D are pre-trained by NRS, and IGWO is used to optimize the fitness function F. With ground-based aerosol lidar data, all-day signal gluing experiments are performed, where IGWO-RSD demonstrates obvious advantages in stability, accuracy and applicability in lidar signal processing compared with NRSWNSGA-II.
Acetylated wood is a durable and dimensionally stable product with many potential applications in exterior timber structures. Research has shown that acetylated wood can be effectively bonded by ...various adhesive types. However, one of the most commonly used adhesives for timber constructions, melamine urea formaldehyde (MUF), shows poor performance in combination with acetylated wood in delamination tests based on cyclic wetting and drying. The hydrophobic acetylated wood surface leads to reduced adhesion due to poorer adhesive wetting and fewer chemical bonds between the resin and the wood polymers. The use of a resorcinol-formaldehyde (RF)-based primer on the acetylated wood surface prior to the application of MUF leads to positive gluing results with both acetylated radiata pine and beech, providing significantly improved resistance to delamination. Radial penetration of the primer and MUF in acetylated wood shows higher penetration compared with untreated wood. In addition, a phenol resorcinol-formaldehyde adhesive system showed high resistance against delamination and can be used for gluing of acetylated wood.
During recent decades, strain gauge-based joint torque sensors have been commonly used to provide high-fidelity torque measurements in robotics. Although measurement of joint torque/force is often ...required in engineering research and development, the gluing and wiring of strain gauges used as torque sensors pose difficulties during integration within the restricted space available in small joints. The problem is compounded by the need for a scalable geometric design to measure joint torque. In this communication, we describe a novel design of a strain gauge-based mono-axial torque sensor referred to as
, the significant features of which are high degree of linearity, symmetry, and high scalability in terms of both size and measuring range. Most importantly, SCTS provides easy access for gluing and wiring of the strain gauges on sensor surface despite the limited available space. We demonstrated that the SCTS was better in terms of symmetry (clockwise and counterclockwise rotation) and more linear. These capabilities have been shown through finite element modeling (ANSYS) confirmed by observed data obtained by load testing experiments. The high performance of SCTS was confirmed by studies involving changes in size, material and/or wings width and thickness. Finally, we demonstrated that the SCTS can be successfully implementation inside the hip joints of miniaturized hydraulically actuated quadruped robot-
. This communication is based on work presented at the 18th International Conference on Climbing and Walking Robots (CLAWAR).
We consider fast oscillating random perturbations of dynamical systems in regions where one can introduce action-angle-type coordinates. In an appropriate time scale, the evolution of first ...integrals, under the assumption that the set of resonance tori is small enough, is approximated by a diffusion process. If action-angle coordinates can be introduced only piece-wise, the limiting diffusion process should be considered on an open-book space. Such a process can be described by differential operators, one in each page, supplemented by some gluing conditions at the binding of the open book.
In the context of high-quality development, environmental issues are being paid more and more attention to, and the release of free formaldehyde has become a major problem that needs to be solved. ...Glueless plywood mainly adopts natural substances as raw materials, without adding chemical products, such as resin adhesives, and it does not contain harmful substances, such as formaldehyde. Glueless plywood is a green product that causes no pollution in the environment and no harm to the human body. In this study, the corresponding weak-phase components in boxwood were pre-delivered by an acidic environmental treatment, and the high-temperature and high-pressure compacting process produced a glueless boxwood panel with excellent water resistance and mechanical properties, while remaining environmentally friendly.
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