We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.
The influence of the running-in process operating parameters on tribological properties of the block-on-disc samples in lubricated sliding conditions is analyzed and discussed in detail. Different running-in regimes are achieved by varying the normal load and sliding speed. After the running-in period, during which the operating parameters are varied, all samples are placed in a working regime under the same set of operating conditions. At the end of the running-in period, as well as at the end of the working period, an analysis of the changes in the surface roughness, microhardness, wear rate, and coefficient of friction is performed. Less desirable properties in terms of wear rate and steady-state coefficient of friction are noticed for the samples that were run-in with the operating conditions which were the same as the working regime operating conditions. In the defined test conditions, it is shown that the intensity of normal load applied during the running-in process has a dominant influence on the amount of wear and coefficient of friction value. It was also shown that the running-in process can significantly improve the roughness of the initially rough contact surfaces. The results of experimental testing indicate that the variation of the operating parameters during the running-in process can be used to improve the working ability of the sliding contact surfaces under the mixed lubrication regime.
We prove that in formal dimension ≤ 20 the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rational homotopy for a simply connected rationally elliptic space.
The question of which manifolds are spin or spin c has a simple and complete answer. In this paper we address the same question for spin h manifolds, which are less studied but have appeared in geometry and physics in recent decades. We determine that the first obstruction to being spin h is the fifth integral Stiefel-Whitney class W 5 . Moreover, we show that every orientable manifold of dimension 7 and lower is spin h , and that there are orientable manifolds which are not spin h in all higher dimensions. We are then led to consider an infinite sequence of generalised spin structures. In doing so, we determine an answer to the following question: is there an integer k such that every manifold embeds in a spin manifold with codimension k?
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