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

Deformation quantization of gerbes

This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.Comment: Revised versio

Foamed glass-ceramic materials based on oil shale by-products

The feasibility and features of the production of foamed glass-ceramic materials based on oil shale ash were investigated. The optimal regime of synthesis found involved the following steps: glass fusion at 1400 °C, preparation of the glass powders and blending with the foaming agent. The foaming was carried out at 900 to 920 °C with a further one-stage crystallization at 790 to 820 °C. It was noted that the admixture of calcium carbonate, as a foaming agent, changed the phase composition of the resulting glass-ceramics by an increased rate of the crystallization process and the intensive formation of gehlenite simultaneously with diopside

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds