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Article
The Detour Polynomials of Ladder Graphs

Authors: Ali A. Ali --- Gashaw A. Mohammed-Saleh
Journal: AL-Rafidain Journal of Computer Sciences and Mathematics مجلة الرافدين لعلوم الحاسوب والرياضيات ISSN: 18154816 Year: 2012 Volume: 9 Issue: 1 Pages: 139-146
Publisher: Mosul University جامعة الموصل

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Abstract

The detour distance between two distinct vertices and of a connected graph is the length of a longest path in . The detour index of is defined by , and the detour polynomial of is . The detour indices and detour polynomials of some ladder graphs are obtained in this paper.

تعرف مسافة الالتفاف D(u,v) بين رأسين مختلفين u وv في بيان متصل G على أنها الطول لأطول درب بين u وv. ويعرف دليل الالتفاف dd(G) على أنه ، كما تعرف متعددة حدود الالتفاف للبيان G كالآتي . تضمن هذا البحث إيجاد متعددة حدود الالتفاف ودليل الالتفاف لأنواع من البيانات المتصلة والتي هي بشكل سُلم (Ladder).

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Article
Femoral neck anteversion & hip rotation range in healthy Iraqi children: A clinical anatomical study

Authors: Ghassan A. Abdulhussein --- Ali. A. Ali --- Sameh S. Akkila
Journal: Mustansiriya Medical Journal مجلة المستنصرية الطبية ISSN: 20701128 22274081 Year: 2012 Volume: 11 Issue: 1 Pages: 33-36
Publisher: Al-Mustansyriah University الجامعة المستنصرية

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Abstract

Background: Femoral neck anteversion (FNA) is a physiological torsion of the femur that plays an important role in the stability & function of the hip joint and has a great impact on the rotational movements of the hip. Abnormal development of the FNA may be associated with a number of orthopaedic problems affecting the hip joint & gait ranging from in-toing gait to disabling osteoarthritis. The assessment of the angle is therefore important in assessing such problems & determining the best course of action in their management.Aims: this study aims at measuring the FNA angle in healthy Iraqi children & examining its impact on hip rotational movements at different age groups.Patients and methods: 36 healthy Iraqi male children divided into 3 age groups were examined clinically for the range of hip rotation & were then subjected to X-ray estimation of the FNA angle of their hips using Ogata’s Biplanar method.Results & conclusions: all the children had FNA angles & hip rotational movements within the normal range for their age with a significant regression in FNA angle with increasing age that may be related to muscular torsional forces applied to growing epiphyses. The FNA angle was inversely proportional to lateral rotation of the hip but directly proportional to medial rotation. Sides to side differences were noticed in tested subjects and were statistically significant in the (8-9 years) age group. This bilateral disparity may normally result from cerebral lateralization or prolonged postural dynamic factors affecting the joints & soft tissues.

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