Browsing by Author "Akkaya T."
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Item The location of the obturator nerve: A three-dimensional description of the obturator canal(2008) Kendir S.; Akkaya T.; Comert A.; Sayin M.; Tatlisumak E.; Elhan A.; Tekdemir I.Satisfactory analgesia cannot be achieved in every obturator nerve block. To attempt to improve the success rate of obturator nerve block, this study describes the detailed anatomy of the obturator region and canal. Eleven (5 female and 6 male) cadavers, totally 22 sides were dissected. Anatomical positions of the structures entering and leaving the canal were defined. The position of the obturator nerve and its branches and their relation with the obturator artery, vein, and with the internal iliac and femoral veins were investigated. A mould of the canal and a model were created. Detailed measurements were performed on the cadavers and models. The obturator canal was in the shape of a funnel compressed from superior to inferior, with anterior and posterior openings. At the entrance of the canal, the nerve lay superiorly; the artery was in the middle, and the vein lay inferiorly. The obturator nerve ran close to the lateral wall of the obturator canal. The distance of lateral wall of obturator canal to the median plane was 41.4 ± 1.1 mm. After leaving the canal, the nerve lay laterally while the anterior branch of the artery was medial. A venous plexus lay between the two structures. The presence of the branches of the obturator artery and vein alongside the obturator nerve may increase the risk of injury to these structures during anaesthetic procedures. The anterior division of the obturator nerve has a close relationship with these vessels. To provide complete analgesia, the obturator nerve should be blocked in the obturator canal or at its external orifice. © Springer-Verlag 2008.Item Legendre series solutions of Fredholm integral equations(Association for Scientific Research, 2010) Yalçinbas S.; Aynigül M.; Akkaya T.A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Legendre coefficients. In addition, some equations considered by other authors are solved in terms of Legendre polynomials and the results are compared. © Association for Scientific Research.Item Boubaker polynomial approach for solving high-order linear differential-difference equations(2012) Akkaya T.; Yalçinbaş S.A numerical method is applied to solve the pantograph equation with proportional delay under the mixed conditions. The method is based on first taking the truncated Boubaker series of the functions in the differential-difference equations and then substituting their matrix forms into the equation. Hence, the result matrix equation can be solved and the unknown Boubaker coefficients can be found approximately. The solution is obtained in terms of Boubaker polynomials. Also, illustrative examples are included to demonstrate the validity and applicability of the technique. The results obtained are compared by the known results. © 2012 American Institute of Physics.Item A numerical approach for solving linear integro-differential-difference equations with Boubaker polynomial bases(Ain Shams University, 2012) Yalçinbaş S.; Akkaya T.In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of mixed linear integro-differential-difference equations under the mixed conditions. The aim of this article is to present the applicability and validity of the technique and the comparisons are made with the existing results. The results demonstrate the accuracy and efficiency of the present work. © 2011 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved.Item Numeric solutions for the pantograph type delay differential equation using First Boubaker polynomials(2013) Akkaya T.; Yalçinbaş S.; Sezer M.A numerical method is applied to solve the pantograph equation with proportional delay under the mixed conditions. The method is based on the truncated First Boubaker series. The solution is obtained in terms of First Boubaker polynomials. Also, illustrative examples are included to demonstrate the validity and applicability of the technique. The results obtained are compared by the known results. © 2013 Elsevier Inc. All rights reserved.