Premature ovarian insufficiency (POI) is defined as a cessation of ovarian function before the age of 40 years. It is associated with hypoestrogenism and loss of residual follicles, both of which lead to menstrual abnormalities, pregnancy failures, and decreased health-related quality of life. The prevalence of POI is estimated at 1% in the general population. Current European Society of Human Reproduction and Embryology (ESHRE) diagnostic criteria include: amenorrhoea or oligomenorrhoea for at least four months and increased follicle-stimulating hormone (FSH) levels > 25 IU/l measured twice (with a four-week interval). The aetiopathogenesis of the disease in most cases remains unexplained. Nevertheless, in some patients with POI, genetic abnormalities, metabolic disorders, autoimmunity, iatrogenic procedures, infections, or environmental factors have been established as underlying causes of the syndrome.

The data from the authors’ earlier investigations show that molecules of zinc dithiophosphate (ZDDP) added to a lubricant can absorb energy emitted by a solid surface, which is where triboreactions occur. If the lubricant contains structures able to conduct energy, the ZDDP reactions can occur even at a relatively large distance from the solid surface, which should increase the effectiveness of ZDDP as an antiwear additive. The purpose of this paper was to verify the thesis that the tribocatalytic effect depends on the ability of the solid surface to emit electrons/energy and the ability of ordered molecular structures, such as carbon nanotubes (CNTs), to conduct energy and, most likely, to enhance the energy transfer. The tribological tests were performed using a TRB3 tribotester for 100Cr6 steel balls and uncoated or a-C:H coated HS6-5-2C steel discs. Polyalphaolefin 8 (PAO8) and PAO8 mixed with ZDDP and CNTs were used as lubricants. The results of the tribological tests suggested that: (a) the effect of the interactions between ZDDP and CNTs was clearly visible; (b) the structure and properties of the solid surface layer had a significant influence on the antiwear action of the ZDDP additive.

a b s t r a c tWe consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition for functions to belong to the class investigated. Finally, we obtain the distortion and the growth theorems. The results presented are a generalization of the results obtained by Gao and Zhou.

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