Browsing by Author "Aslan, E"

Now showing 1 - 20 of 27
  • No Thumbnail Available
    Item
    On the numerical solution of fractional differential equations with cubic nonlinearity via matching polynomial of complete graph
    Kürkçü, ÖK; Aslan, E; Sezer, M
    This study deals with a generalized form of fractional differential equations with cubic nonlinearity, employing a matrix-collocation method dependent on the matching polynomial of complete graph. The method presents a simple and efficient algorithmic infrastructure, which contains a unified matrix expansion of fractional-order derivatives and a general matrix relation for cubic nonlinearity. The method also performs a sustainable approximation for high value of computation limit, thanks to the inclusion of the matching polynomial in matrix system. Using the residual function, the convergence and error estimation are investigated via the second mean value theorem having a weight function. In comparison with the existing results, highly accurate results are obtained. Moreover, the oscillatory solutions of some model problems arising in several applied sciences are simulated. It is verified that the proposed method is reliable, efficient and productive.
  • No Thumbnail Available
    Item
    Algorithm of Neighbor Isolated Scattering Number
    Tosun, MA; Aslan, E; Borandag, E
    Network security and reliability is an essential part of computer networks. Network security has had to improve due to hackers. Business continuity is another reason for improvement. Networks can be modeled with graphs. Various parameters exist to measure the vulnerability of graphs, and hence of networks. In this paper, we consider neighbor isolated scattering number and an algorithm has been developed for the proposed vulnerability measurement parameter, which we recommend to measure for any graph and the algorithm is analyzed by software code metrics and have been shown to be useful. Thus, it has been concluded that humanpower will be saved by using an algorithm while measuring vulnerability for any graph.
  • No Thumbnail Available
    Item
    An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays
    Kürkçü, ÖK; Aslan, E; Sezer, M
    This study considers the space-time fractional partial differential equations with multi delays under a unique formulation, proposing a numerical method involving advanced matrix system. This matrix system is made up of the matching polynomial of complete graph together with fractional Caputo and Jumarie derivative types. Also, the derivative types are scrutinized to determine which of them is more proper for the method. Convergence analysis of the method is established via an average value of residual function using double integrals. The obtained solutions are improved with the aid of a residual error estimation. A general computer program module, which contains few steps, is developed. Tables and figures prove the efficiency and simplicity of the method. Eventually, an algorithm is given to illustrate the basis of the method.
  • No Thumbnail Available
    Item
    A fast numerical method for fractional partial integro-differential equations with spatial-time delays
    Aslan, E; Kürkçü, ÖK; Sezer, M
    This study aims to efficiently solve the space-time fractional partial integro-differential equations with spatial-time delays, employing a fast numerical methodology dependent upon the matching polynomial of complete graph and matrix-collocation procedure. This methodology provides a sustainable approach for each computation limit since it arises from the durable graph structure of complete graph and fractional matrix relations. The convergence analysis is established using the residual function of mean value theorem for double integrals. An error estimation is also implemented. All computations are performed with the aid of a unique computer program, which returns the desired results in seconds. Some specific numerical problems are tested to discuss the applicability of the method in tables and figures. It is stated that the method stands for fast, simple and highly accurate computation. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
  • No Thumbnail Available
    Item
    An inventive numerical method for solving the most general form of integro-differential equations with functional delays and characteristic behavior of orthoexponential residual function
    Kürkçü, ÖK; Aslan, E; Sezer, M
    In this study, we constitute the most general form of functional integro-differential equations with functional delays. An inventive method based on Dickson polynomials with the parameter- along with collocation points is employed to solve them. The stability of the solutions is simulated according to an interval of the parameter-. A useful computer program is developed to obtain the precise values from the method. The residual error analysis is used to improve the obtained solutions. The characteristic behavior of the residual function is established with the aid of the orthoexponential polynomials. We compare the present numerical results of the method with those obtained by the existing methods in tables.
  • No Thumbnail Available
    Item
    A novel hybrid method for solving combined functional neutral differential equations with several delays and investigation of convergence rate via residual function
    Kürkçü, ÖK; Aslan, E; Sezer, M
    In this study, we introduce a novel hybrid method based on a simple graph along with operational matrix to solve the combined functional neutral differential equations with several delays. The matrix relations of the matching polynomials of complete and path graphs are employed in the matrix-collocation method. We improve the obtained solutions via an error analysis technique. The oscillation of them on time interval is also estimated by coupling the method with Laplace-Pade technique. We develop a general computer program and so we can efficiently monitor the precision of the method. We investigate a convergence rate of the method by constructing a formula based on the residual function. Eventually, an algorithm is described to show the easiness of the method.
  • No Thumbnail Available
    Item
    An investigation on the seasonal variations of the biomarkers of oxidative stress response and their correlations to Polonium-210 in mussel (Mytilus galloprovincialis) and common sole (Solea solea) from Izmir Bay, Turkey
    Aslan, E; Görgün, AU; Katalay, S; Filizok, I; Becerik, S; Aydemir, T
    It is well known that the marine organisms are used as biological indicators for environmental pollution studies. Among these studies, the research on oxidative stress has been increasing in recent years. In this study, mussels (Mytilus galloprovincialis) and fish (Solea solea) samples were collected seasonally from inciralti, Izmir, Turkey. This station was in an area where fishing is carried out for human consumption. The relationship between Po-210 and oxidative stress markers (lipid peroxidation (LPO), H2O2 and proline) was investigated in the mussel tissue (digestive gland, gills) and fish tissue (liver, gills) samples. The present study indicated that H2O2 accumulated with increasing Po-210 concentration in mussel samples. Statistically significant correlation were found between H2O2 and Po-210 and LPO and proline in mussel samples. This correlation between LPO and proline can be attributed to common environmental parameters (other than Po-210) affecting expression of both LPO and proline levels. There was not a significant correlation between Po-210 and LPO levels. Similarly, a significant correlation was not found between Po-210 and proline.
  • No Thumbnail Available
    Item
    An integrated numerical method with error analysis for solving fractional differential equations of quintic nonlinear type arising in applied sciences
    Kürkçü, ÖK; Aslan, E; Sezer, M
    In this study, fractional differential equations having quintic nonlinearity are considered by proposing an accurate numerical method based on the matching polynomial and matrix-collocation system. This method provides an integration between matrix and fractional derivative, which makes it fast and efficient. A hybrid computer program is designed by making use of the fast algorithmic structure of the method. An error analysis technique consisting of the fractional-based residual function is constructed to scrutinize the precision of the method. Some error tests are also performed. Figures and tables present the consistency of the approximate solutions of highly stiff model problems. All results point out that the method is effective, simple, and eligible.
  • No Thumbnail Available
    Item
    A novel graph-operational matrix method for solving multidelay fractional differential equations with variable coefficients and a numerical comparative survey of fractional derivative types
    Kürkçu, OK; Aslan, E; Sezer, M
    In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
  • No Thumbnail Available
    Item
    A Numerical Approach Technique for Solving Generalized Delay Integro-Differential Equations with Functional Bounds by Means of Dickson Polynomials
    Kürkçü, OK; Aslan, E; Sezer, M; Ilhan, Ö
    In this study, we have considered the linear classes of differential-(difference), integro-differential-(difference) and integral equations by constituting a generalized form, which contains proportional delay, difference, differentiable difference or delay. To solve the generalized form numerically, we use the efficient matrix technique based on Dickson polynomials with the parameter-a along with the collocation points. We also encode the useful computer program for susceptibility of the technique. The residual error analysis is implemented by using the residual function. The consistency of the technique is analyzed. Also, the numerical results illustrated in tables and figures are compared.
  • No Thumbnail Available
    Item
    Multi-level reranking approach for bug localization
    Kilinç, D; Yücalar, F; Borandag, E; Aslan, E
    Bug fixing has a key role in software quality evaluation. Bug fixing starts with the bug localization step, in which developers use textual bug information to find location of source codes which have the bug. Bug localization is a tedious and time consuming process. Information retrieval requires understanding the programme's goal, coding structure, programming logic and the relevant attributes of bug. Information retrieval (IR) based bug localization is a retrieval task, where bug reports and source files represent the queries and documents, respectively. In this paper, we propose BugCatcher, a newly developed bug localization method based on multi-level re-ranking IR technique. We evaluate BugCatcher on three open source projects with approximately 3400 bugs. Our experiments show that multi-level reranking approach to bug localization is promising. Retrieval performance and accuracy of BugCatcher are better than current bug localization tools, and BugCatcher has the best Top N, Mean Average Precision (MAP) and Mean Reciprocal Rank (MRR) values for all datasets.
  • No Thumbnail Available
    Item
    THE AVERAGE LOWER REINFORCEMENT NUMBER OF A GRAPH
    Turaci, T; Aslan, E
    Let G = (V (G), E(G)) be a simple undirected graph. The reinforcement number of a graph is a vulnerability parameter of a graph. We have investigated a refinement that involves the average lower reinforcement number of this parameter. The lower reinforcement number, denoted by r(e*) (G), is the minimum cardinality of reinforcement set in G that contains the edge e* of the complement graph G. The average lower reinforcement number of G is defined by r(av)(G) = 1/ |E(G)| Sigma(e*)is an element of E((G) over bar) r(e*) (G). In this paper, we define the average lower reinforcement number of a graph and we present the exact values for some well-known graph families.
  • No Thumbnail Available
    Item
    Computing the weighted neighbor isolated tenacity of interval graphs in polynomial time
    Aslan, E; Tosun, MA
    Weighted graphs in graph theory are created by weighing different values depending on the importance of connections or centers in a graph model. Networks can be modeled with graphs such that the devices and centers correspond to the vertices and connections correspond to the edges. In these networks, weight can be assigned to the vertices for the workload and importance of the devices and centers, so that planning such as security and cost can be made in advance in the design of the network. Network reliability and security is an important issue in the computing area. There are several parameters for vulnerability measurement values of these networks modeled with graphs. We recommend the weighted conversion of the neighbor isolated tenacity parameter for this topic. It is known that tenacity, which is the basis of this parameter, is NP-hard. But polynomial solutions can be created in interval graphs, which is a special graph from the perfect graph class. In this article, polynomial time algorithm is given to calculate weighted neighbor isolated tenacity of the interval graphs.
  • No Thumbnail Available
    Item
    The average binding number of graphs
    Aslan, E
    The binding number is a measure of the vulnerability of a graph. We investigate a refinement that involves the average of this parameter. Like the binding number itself, the average binding number bindav (G) of G measures the vulnerability of a graph, which is more sensitive. In this study, some bounds of the average binding number of some special graphs are obtained. Furthermore some results about the average binding number of graphs obtained from graph operations are also provided.
  • No Thumbnail Available
    Item
    Edge-Neighbor-Rupture Degree of Graphs
    Aslan, E
    The edge-neighbor-rupture degree of a connected graph G is defined to be ENR(G) = max{omega(G - S) - vertical bar S vertical bar - m(G - S) : S subset of E(G), omega(G - S) >= 1}, where S is any edge-cut-strategy of G, omega (G - S) is the number of the components of G - S, and m(G - S) is the maximum order of the components of G - S. In this paper, the edge-neighbor-rupture degree of some graphs is obtained and the relations between edge-neighbor-rupture degree and other parameters are determined.
  • No Thumbnail Available
    Item
    Feasible Sanitary Sewer Network Generation Using Graph Theory
    Turan, ME; Bacak-Turan, G; Cetin, T; Aslan, E
    A graph theory-based methodology is proposed for the sewer system optimization problem in this study. Sewer system optimization includes two subproblems: layout optimization and hydraulic design optimization, which can be solved independently or solved simultaneously. No matter which method is chosen for the solution of the optimization problem, a feasible layout that satisfies the restrictions of the sewer system must be obtained in any step of the solution. There are two different layout options encountered: the layouts containing all sewer links and the layouts not containing all sewer links. The method proposed in this study generates a feasible sewer layout that contains all sewer links and satisfies all restrictions of a sanitary sewer system by using graph theory without any additional strategies unlike other studies. The method is applied to two different case studies. The results of the case studies have shown that graph theory is well applicable to sewer system optimization and the methodology proposed based on it is capable of generating a feasible layout. This study is expected to stimulate the use of graph theory on similar studies.
  • No Thumbnail Available
    Item
    A Comparison Between Edge Neighbor Rupture Degree and Edge Scattering Number in Graphs
    Kürkcü, ÖK; Aslan, E
    The vulnerability measure of a graph or a network depends on robustness of the remained graph, after being exposed to any intervention or attack. In this paper, we consider two edge vulnerability parameters that are the edge neighbor rupture degree and the edge scattering number. The values of these parameters of some specific graphs and their graph operations are calculated. Thus, we analyze and compare which parameter is distinctive for the different type of graphs by using tables.
  • No Thumbnail Available
    Item
    MEAN RUPTURE DEGREE OF GRAPHS
    Aslan, E; Bacak-Turan, G
    The vulnerability shows the resistance of the network until communication breakdown after the disruption of certain stations or communication links. We introduce a new graph parameter, the mean rupture degree. Let G be a graph of order p and S be a subset of V(G). The graph G-S contains at least two components and if each one of the components of G-S have orders p(1), p(2), ..., p(k), then m(G-S) = Sigma(k)(i=1)p(i)(2)/Sigma(k)(i=1)p(i). Formally, the mean rupture degree of a graph G, denoted mr(G), is defined as mr(G)= max{omega(G-S)-vertical bar S vertical bar-m(G-S): S subset of V(G), omega(G-S)>1} where omega(G-S) denote the number of components. In this paper, the mean rupture degree of some classes of graphs are obtained and the relations between mean rupture degree and other parameters are determined.
  • No Thumbnail Available
    Item
    Neighbour isolated scattering number of graphs
    Aslan, E
    The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined to be NIS(G) = max{i(G/X)-vertical bar X vertical bar : i(G/X) >= 1} where the maximum is taken over all X, the cut strategy of G, and i(G/X) is the number of components which are isolated vertices of G/X. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. The relations between neighbour isolated scattering number and other parameters are determined and the neighbour isolated scattering number of trees and other families are obtained. We also give some results for the neighbour isolated scattering number of the graphs obtained by some graph operations.
  • No Thumbnail Available
    Item
    The Average Lower Connectivity of Graphs
    Aslan, E
    For a vertex V of a graph.., the lower connectivity, denoted by S-v(G), is the smallest number of vertices that contains v and those vertices whose deletion from.. produces a disconnected or a trivial graph. The average lower connectivity denoted by kappa(av)(G) is the value (Sigma(v epsilon V(G))s(v)(G))/vertical bar V(G)vertical bar. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.