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The new modified Ishikawa iteration method for the approximate solution of different type of differential equations
Necdet BILDIK, Yasemin BAKIR and Ali MUTLU
Fixed Point Theory and Applications , 2013, DOI: 10.1186/1687-1812-2013-52
Abstract: In this article, the new Ishikawa iteration method is present to find the approximate solution of ordinary differential equation having initial condition. Additionally, some numerical examples with initial conditions are given to show the properties of the iteration method. Furthermore, the results of absolute errors are compared with Euler, Runge-Kutta and Picard iteration method. Finally, the present method namely the new modified Ishikawa iteration method is seen to be very effective and efficient in order to solve different type of the problem.
Computing Hypercrossed Complex Pairings in Digital Images
Simge ?ztun?,Ali Mutlu,Necdet Bildik
Abstract and Applied Analysis , 2013, DOI: 10.1155/2013/675373
Abstract: We consider an additive group structure in digital images and introduce the commutator in digital images. Then we calculate the hypercrossed complex pairings which generates a normal subgroup in dimension 2 and in dimension 3 by using 8-adjacency and 26-adjacency. 1. Introduction In this paper we denote the set of integers by . Then represents the set of lattice points in Euclidean -dimensional spaces. A finite subset of with an adjacency relation is called a digital image. Definition 1 (see [1, 2]). Consider the following.(1)Two points and in are 2-adjacent if .(2)Two points and in are 8-adjacent if they are distinct and differ by at most 1 in each coordinate.(3)Two points and in are 4-adjacent if they are 8-adjacent and differ by exactly one coordinate.(4)Two points and in are 26-adjacent if they are distinct and differ by at most 1 in each coordinate.(5)Two points and in are 18-adjacent if they are 26-adjacent and differ in at most two coordinates.(6)Two points and in are 6-adjacent if they are 18-adjacent and differ by exactly one coordinate. Definition 2. Let be a subset of a digital image. A simplicial group in digital images consists of a sequence of groups and collections of group homomorphisms and , , that satisfies the following axioms: Definition 3. Given a simplicial group with -adjacency, the Moore complex of is the chain complex defined by with induced from by restriction. The th homology group of the Moore complex of is 2. Hypercrossed Complex Pairings in Digital Images First of all we adapt ideas from Carrasco and Cegarra [3–5] to get the construction in digital images. We define a set consisting of pairs of elements from with and , with respect to lexicographic ordering in where and . Consider the following diagram: (4) where and define and as and . Since a digital image has the additive group structure, define the commutator as Thus The normal subgroup of is generated by the elements of the form where and . Theorem 4. 2-dimensional normal subgroup with 8-adjacency is generated by the elements of the form Proof. Let and for . For and , Thus and this is the element generating normal subgroups. Proposition 5. 3-dimensional normal subgroup with 26-adjacency is generated by the elements of the following forms:(i) ,(ii) ,(iii) ,(iv) ,(v) ,(vi) . Proof. For the possible pairings are the following:(i) ,(ii) ,(iii) ,(iv) ,(v) ,(vi) .For all and the corresponding generators of are the following with and for , : (i) (ii) For all and and considering the map , the corresponding generator of is (iii) For all , and for the corresponding generators of
New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation
Abdon Atangana,Necdet Bildik,S. C. Oukouomi Noutchie
Abstract and Applied Analysis , 2014, DOI: 10.1155/2014/740248
Abstract: We put side by side the methodology of two comparatively new analytical techniques to get to the bottom of the system of nonlinear fractional modified Kawahara equation. The technique is described and exemplified with a numerical example. The dependability of both methods and the lessening in computations give these methods a wider applicability. In addition, the computations implicated are very simple and undemanding. 1. Introduction Within the scope of fractional calculus in the recent decade several scholars have modeled physical and engineering problems. Respective scholar while dealing with real world problems found out that it is worth describing these phenomena with the idea of derivatives with fractional order. While searching the literature, we found out that, this concept of noninteger order derivative not only has been intensively used but also has played an essential role in assorted branches of sciences including but not limited to hydrology, chemistry, image processing, electronics and mechanics; the applicability of this philosophy can be found in [1–10]. In the foregone respective decennial, the research of travelling-wave solutions for nonlinear equations has played a crucial character in the examination of nonlinear physical phenomena. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction, and convection are very important in nonlinear wave equations. Concepts like solitons, peakons, kinks, breathers, cusps, and compactons have now been thoroughly investigated in the scientific literature [11–13]. Various powerful mathematical methods such as the inverse scattering method, bilinear transformation [14], the tanh-sech method [15, 16], extended tanh method [16], Exp-function method [17–19], sine-cosine method [20] Adomian decomposition method [21], Exp-function method [22], homotopy perturbation method [23] have been proposed for obtaining exact and approximate analytical solutions. The purpose of this paper is to examine the approximated solution of the nonlinear fractional modified Kawahara equation, using the relatively new analytical method, the Homotopy decomposition method (HDM), and the Sumudu transform method. The fractional partial differential equations under investigation here are given below as subject to the initial condition The outstanding of this paper is prearranged as follows. In Section 2 we present a succinct history of the fractional derivative order and their properties. We present the basic ideal of the HDM and the STM for solving high order nonlinear fractional partial differential equations. We
Vazoactive Effects of Oxidative Stress Elicited by Hydrogen Peroxide in the Human Umbilical Artery: An in Vitro Study  [PDF]
Ipek Duman, Necdet Dogan
Pharmacology & Pharmacy (PP) , 2011, DOI: 10.4236/pp.2011.24045
Abstract: The vasoactive effects of oxidative stress induced by hydrogen peroxide (H2O2) on human umbilical artery strips as well as the possible mechanisms involved are studied. Contraction responses to cumulative H2O2 (10–7 M-3 × 10–2 M) in endothelium intact and denuded umbilical arteries and responses to cumulative H2O2 after incubation with L-NAME (10–4 M) (n = 8), indomethacin (10–5 M) (n = 8) and verapamil (10–6) (n = 8) were recorded. Responses elicited with cumulative H2O2 in Ca2+ free extracellular medium and the responses to cumulative Ca2+ (10–4 M-2 × 10–3 M) after H2O2 (10–3 M) induced contraction were also studied. The Emax for each experiment was calculated. p <0.05 was considered as significant. H2O2 elicited contraction was greater in endothelium denuded artery strips compared to endothelium intact strips (p < 0.05). Compared to control, incubation with L-NAME significantly augmented (p < 0.05), while verapamil and indomethacin inhibited the contractions elicited by cumulative H2O2 (p < 0.05). Ca2+ free extracellular medium caused decreases in cumulative H2O2 elicited contractions and cumulative Ca2+ caused concentration dependent increases in the contraction caused by a single bolus of H2O2 (p < 0.05). Exposure to H2O2 causes concentration-dependent constriction in human umbilical arteries. The presence of the endothelium and NOS enzyme activation influences the H2O2 responses. Removal of the endothelium increases the H2O2 elicited contractions more than incubation with L-NAME suggesting beside NO, other endothelial vasodilators are also involved in vascular tonus of the umbilical arteries. Both intracellular and extracellular Ca2+ ions and constrictor cyclooxygenase metabolites play a
Detection of Apoptosis in Experimental Fibrosarcoma Using DNA Fragmentation and Immunohystochemical Methods
Hasan Aksit,Aysegul Bildik
Journal of Animal and Veterinary Advances , 2012, DOI: 10.3923/javaa.2012.3054.3058
Abstract: Fibrosarcoma is driving from mesenchimal tissue. It is one of the malign tumors and usually seen in cats and dogs however, it can be encountered in all animals. Apoptosis used for eliminating of cells which are functioning not properly. Recent studies on tumors showed that there is a connection between cancers and apoptosis. In this study, apoptosis in fibrosarcomas induced by 3-methylcholanthrene using immunuhystochemical and ELISA Methods was investigated. In order to induce fibrosarcoma in rats at the beginning of the experiment animals were injected subcutaneously on the neck with 0.2 mg 3-methylcholanthrene solved in 0.25 mL sesame oil. During the experiment took between 150-210 days depending on the appearance of tumor tissue. At the end of the experiment animals were killed under the ether anesthesia and necropsy is performed. DNA fragments of tumor tissue cell were analized using ELISA, localisation of Bcl-2 and Bax was determined by immunohystochemical method. Immunohistochemically there was a lot of Bcl-2 and Bax positive cells. Contrary to this in control animals there was rarely. Furthermore, the absorbance of DNA fragmentation of experimental, animals was 4 times higher than that of controls. This data indicates that in the tumor tissues it is observed some cells programmed to death by apoptosis but the others not.
Proyecciones (Antofagasta) , 2008, DOI: 10.4067/S0716-09172008000100006
Abstract: let n be a positive integer. we prove with the best possible constants this refines and extends a result of sandor and debnath, who proved that the double inequality holds with a = 0 and ? = 1
Proyecciones (Antofagasta) , 2008,
Abstract: Let n be a positive integer. We prove with the best possible constants This refines and extends a result of Sandor and Debnath, who proved that the double inequality holds with a = 0 and = 1
Aprender de la educación en arquitectura
Necdet Teymur
DEARQ : Journal of Architecture , 2011,
Abstract: El autor plantea una serie de preguntas fundamentales alrededor de la investigación sobre educación en arquitectura, o la ausencia de ella. Después de una introducción, desglosa las preguntas: por qué investigar sobre educación en arquitectura? Cómo estudiar la educación en arquitectura? Qué se debe investigar? Comenta las falencias, oportunidades y riesgos de la educación en arquitectura y la investigación sobre ella, y concluye que la generación de conocimiento sobre la arquitectura y su educación ayudará a construir la arquitectura como disciplina, a la vez que la misma actividad de investigar lleva a un entendimiento más profundo de la arquitectura y del mundo.
Evaluation of Activities in Primary Education Programme with The Teachers’ Views (Sample of Sinop Province)
Necdet AYKA?
Journal of Kirsehir Education Faculty , 2007,
Abstract: This research, aims to investigate the concept of activity on the basis of learning-teaching duration inaccordance with teachers’ views, teachers guide and class materials in the primary education programme put in to practice in 2005- 2006. The research has two subjects. The first one is the quantitative subject aiming to determine the teachers’ views, the second is theoretical subject aiming to analyze the guide books and class metarials. The quantitative research, aiming to determine the teachers’ ideas is consisted of 184 teachers in total in the center and in the central villages of Sinop. The exemplification in this research is occupied by means of 86 teachers applying the teachers’ views determinating scale. In the research as a tool to collect data, determining teachers’ views scale prepared in 5 likert-type scale with 18 articles has been used. Analyzing with SPSS programme, the data gained from the scale has been stated as frequency and percentage. Theoretical dimension examining teachers’ guide and lesson metarials to put the teachers’ views on a objective base, aims to examine teachers guide books and lesson materials analytically and display the base of teachers’ views. It is stated that most of the teachers present their views in that way: They feel themselves insufficent to applythe activities,the physical opportunities of the schools and the facilities are not enough to apply some activities, the classes are crowded, the activities are not student-centered and active teaching methods are not used in the activities.
Treatment of Antimicrobial-Resistant Gram-Negative Infections in Children
Necdet Kuyucu
Cocuk Enfeksiyon Dergisi , 2009,
Abstract: With the changing epidemiology of either community-acquired or nosocomial infections, microbial resistance patterns have been rapidly changing. The increasingly daunting problem of antimicrobial resistance has led to an intense focus on optimization of antibiotic therapy. Recent epidemiological studies suggest an increase in nosocomial infections caused by gram-negative bacteria, particularly Klebsiella spp., Escherichia coli, Pseudomonas aeruginosa, and Acinetobacter spp. Optimization of therapy against these organisms starts with the initial empirical antibiotic choice. Surveillance data and hospital or unit antibiograms may inform this decision. Several nosocomial pediatric infectious diseases that some gram-negative bacteria will be reviewed briefly in this article with regard to microbial resistance patterns and treatment approaches.
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