The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers

The distant graph $G = G(\mathbb{P}(Z),\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued fractions. In case the minimal path is non-unique, all the possible splitting are described which allows us to give necessary and sufficient conditions for existence of a unique shortest path.Comment: 20 pages, 4 figures, Bulletin of the Malaysian Mathematical Sciences Society, online 201

Neumann property in the extended modular group and maximal nonparabolic subgroups of the modular group

It is know that any Neumann subgroup of the modular group is maximal non-parabolic. The question arises as to whether these are the only maximal non-parabolic subgroups. The wild class of maximal, non-parabolic, not Neumann subgroups of the modular group was constructed by Brenner and Lyndon. The new construction of such a class is presented. Those groups are obtained as subgroups of elements of positive determinant of any Neumann subgroup of the extended modular group (the notion which we introduce in the paper) and in this sens they are as "close" as possible to Neumann subgroups of the modular group.Comment: 1 figur

The incidence of acute pancreatitis in children hospitalized with abdominal pain in Pediatric Surgery Clinic in Bydgoszcz

Lewicka Marta, Barczykowska Ewa, Jaworska Aleksandra, Daniluk-Matraś Irena, Kurylak Andrzej. The incidence of acute pancreatitis in children hospitalized with abdominal pain in Pediatric Surgery Clinic in Bydgoszcz. Journal of Education, Health and Sport. 2015;5(10):29-42. ISSN 2391-8306. DOIhttp://dx.doi.org/10.5281/zenodo.31917 http://ojs.ukw.edu.pl/index.php/johs/article/view/2015%3B5%2810%29%3A29-42 https://pbn.nauka.gov.pl/works/647539 Formerly Journal of Health Sciences. ISSN 1429-9623 / 2300-665X. Archives 2011–2014http://journal.rsw.edu.pl/index.php/JHS/issue/archive   Deklaracja. Specyfika i zawartość merytoryczna czasopisma nie ulega zmianie. Zgodnie z informacją MNiSW z dnia 2 czerwca 2014 r., że w roku 2014 nie będzie przeprowadzana ocena czasopism naukowych; czasopismo o zmienionym tytule otrzymuje tyle samo punktów co na wykazie czasopism naukowych z dnia 31 grudnia 2014 r. The journal has had 5 points in Ministry of Science and Higher Education of Poland parametric evaluation. Part B item 1089. (31.12.2014). © The Author (s) 2015; This article is published with open access at Licensee Open Journal Systems of Kazimierz Wielki University in Bydgoszcz, Poland and Radom University in Radom, Poland Open Access. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. The authors declare that there is no conflict of interests regarding the publication of this paper. Received: 02.08.2015. Revised 05.09.2015. Accepted: 29.09.2015.   The incidence of acute pancreatitis in children hospitalized with abdominal pain in Pediatric Surgery Clinic in Bydgoszcz   Marta Lewicka1, Ewa Barczykowska1, Aleksandra Jaworska2, Irena Daniluk‑Matraś2, Andrzej Kurylak1   1Zakład Pielęgniarstwa Pediatrycznego, Collegium Medicum w Bydgoszczy 2Oddział Kliniczny Chirurgii Ogólnej i Onkologicznej Dzieci i Młodzieży, SU nr 1 im. A. Jurasza w Bydgoszczy   Abstract Introduction The condition most frequently reported by children is abdominal pain, posing a substantial diagnostic problem. In paediatric population, acute pancreatitis occurs much less frequently than in adults. Aim of the study The aim of the study was to assess rate of acute pancreatitis in children accepted to hospital for abdominal pains. Material and methods The study was of a retrospective nature. 629 medical histories of children hospitalized in University Hospital No. 1 in Bydgoszcz for abdominal pains and/or acute pancreatitis were analyzed. Demographic data (sex, age, residence) and season of patients' admission were included in the study. Results The study reveals, that hospital admissions for abdominal pain more frequently regarded boys – 352 (55.96%) than girls – 277 (44.04%). Children of urban background formed 57.39% and those of rural background – 42.61%. In the studied group, acute pancreatitis concerned girls more frequently than boys (8.7% vs 3.7%). No statistical relationship was proven between the age and the acute pancreatitis occurrence. The average age of children with acute pancreatitis amounted to 11.02 years. Every third instance of acute pancreatitis was diagnosed in spring (32.4%), and every fifth (18.9%) in winter. Conclusions • An increase is observed in the number of children's hospital admissions for abdominal pains. Admissions for abdominal pains formed an average of one fifth of all admissions.. • A decrease in acute pancreatitis occurrence is observed in hospitalized children. • Acute pancreatitis occurred twice as often in girls than in boys.   Keywords: children, pain, abdominal pain, pain evaluation, pancreas, pancreatitis, acute pancreatitis