A Hilbert bundle description of differential K-theory

We give an infinite dimensional description of the differential K-theory of a manifold $M$. The generators are triples $[H, A, \omega]$ where $H$ is a ${\bf Z}_2$-graded Hilbert bundle on $M$, $A$ is a superconnection on $H$ and $\omega$ is a differential form on $M$. The relations involve eta forms. We show that the ensuing group is the differential K-group $\check{K}^0(M)$. In addition, we construct the pushforward of a finite dimensional cocycle under a proper submersion with a Riemannian structure. We give the analogous description of the odd differential K-group $\check{K}^1(M)$. Finally, we give a model for twisted differential K-theory.Comment: final version, 52 page

Prediction model for the pressing process in an innovative forming joints technology for woodworking

To improve the efficiency of the joints formation, a new method of pressing in the longitudinal direction is proposed. This paper presents a predictive model for the pressing force depending on the state of the wood and the parameters of the pressed mortise. The most significant factors are the width of the mortise and the moisture content of the wood. Interestingly, the depth of the mortise formation is a less significant factor, which means that the pressing technology will allow to form a long glue line and accordingly high joint strength due to sufficient profile length. In the test range of factors, the best results in terms of energy costs are shown by a minimum mortise width of 4 mm. Further research should be devoted to the study of the formation of small width mortises (4 mm or less) and the investigation of their quality. © 2019 Published under licence by IOP Publishing Ltd