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  • Author: Zbigniew Król x
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In this paper the final stages of the historical process of the emergence of actual infinity in mathematics are considered. The application of God’s point of view – i.e. the possibility to create mathematics from a divine perspective, i.e. from the point of view of an eternal, timeless, omniscience and unlimited subject of cognition – is one of the main factors in this process. Nicole Oresme is the first man who systematically used actual infinity in mathematical reasoning, constructions and proofs in geometry.


In the paper, the measurement of the marine diesel engine crankshaft residual stresses is presented. The hole drilling strain gauge was chosen because of its simplicity and low cost. Moreover, deflection calculation was made for the load corresponding to its weight and the concentrated force in the chosen bearing conditions. Deflection of the journal and bending rigidity under the concentrated force was calculated as well. In that case, the crankshaft was supported in the neighbouring crank journals. The reduced stresses were calculated according to the Huber – Mises hypothesis. The residual stresses were measured in the marine diesel engine crankshaft type 12V38 after the finishing, with the hole-drilling method. It was found that the residual stresses reach the maximal value of 86 MPa, but for 50% of measuring points, the residual stresses did not exceed the value of 20 MPa. The squeezing stresses were found to be dominant. The measurement results provided important data for further consideration, especially for the correction of the bending deformation of the produced crankshaft.


Background: Juvenile idiopathic arthritis (JIA) is a heterogenic group of chronic inflammatory connective tissue diseases of unknown aetiology in children up to 16 years of age. Aim: The aim of this study was to analyse the incidence, clinical presentation and laboratory findings in children with JIA in Malopolska region.

Materials and methods: A retrospective analysis included all children with JIA (N=251) hospitalized in the two reference rheumatology centres covering Malopolska region (Poland), between July 2007 and December 2010.

Results: The annual incidence of JIA in Malopolska region was estimated at 9.5 per 100 000 children. Oligoarthritis (54.9%) was the most common category in all age groups with a tendency to decrease with age; from 71.4 % in children aged 1-6 years; 55.7% in aged 7-12 years to 39.3 % in aged 13-16 years. The frequency of polyarthritis and enthesitis-related arthritis was greater in adolescents (29.2 % and 22.5 %, respectively). HLA-B27 antigen and uveitis were most frequently found in children with enthesitis-related arthritis (58% and 18.5 %, respectively).

Conclusions: The study suggests the improvement of diagnostic capacity of JIA during the last decade in Poland. In accordance with the existing data diverse clinical presentation of JIA categories and laboratory characteristics were proven.


There is no clear evidence that vitamin D effectively improves physical capacity in high-level athletes. The aim of this study was to confirm that vitamin D supplementation of soccer players during eight-week high-intensity training would have a significant effect on their aerobic capacity. The subjects were divided into two groups: the experimental one that was supplemented with vitamin D (SG, n = 20), and the placebo group (PG, n = 16), not supplemented with vitamin D. All the players were subjected to the same soccer training described as High-Intensity Interval Training (HIIT). The data of the vitamin D level, PWC170, lactate threshold (LT) were collected just before and after the intervention. A significant increase in vitamin D concentration (119%) was observed in the supplemented group, while the non-supplemented group showed a decrease of 8.4%. The studied subjects improved VO2max results by 20% in the SG, and by 13% in the PG. The improvement in velocity at the LT was similar in both groups. Results of this study show that vitamin D can have a positive, though moderate, effect on aerobic performance in players subjected to high-intensity training in the form of small-sided games for 8 weeks.