Matematik Bölümü Makale Koleksiyonu

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https://hdl.handle.net/20.500.12713/2070

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n-roots on MV-algebras
(Elsevier B.V., 2024) Dvure?enskij, A.; Zahiri, O.; Shenavaei, M.; Borzooei, R.A.
We introduce and investigate n-roots in the context of MV-algebras as a generalization of square roots introduced in [16]. We outline their main properties and establish that the class of MV-algebras with n-roots, MVnr, forms a variety. Next, we introduce the concept of strict n-roots and demonstrate an equivalence between MVnr and the class of n-divisible unital ?-groups. It helped us to show that each MV-algebra with an n-root is a direct product of an n-strict MV-algebra and a Boolean algebra. Finally, we delve into the connection between strongly atomless MV-algebras and MV-algebras with strict n-roots, demonstrating that in the context of MVnr, these concepts are equivalent. © 2024
Data envelopment analysis for scale elasticity measurement in the stochastic case: with an application to Indian banking
(Springer Science and Business Media Deutschland GmbH, 2023) Amirteimoori, Alireza; Sahoo, Biresh K.; Mehdizadeh, Saber
In the nonparametric data envelopment analysis literature, scale elasticity is evaluated in two alternative ways: using either the technical efficiency model or the cost efficiency model. This evaluation becomes problematic in several situations, for example (a) when input proportions change in the long run, (b) when inputs are heterogeneous, and (c) when firms face ex-ante price uncertainty in making their production decisions. To address these situations, a scale elasticity evaluation was performed using a value-based cost efficiency model. However, this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data. Therefore, in this study, we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty. An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years (1998–2005) was made to compare inferences about their efficiency and scale properties. The key findings are as follows: First, both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints. However, both models yield the same results at a tolerance level of 0.5, implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks. Second, the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart. Third, public banks exhibit higher efficiency than private and foreign banks. Finally, public and old private banks mostly exhibit either decreasing or constant returns to scale, whereas foreign and new private banks experience either increasing or decreasing returns to scale. Although the application of our proposed stochastic model is illustrative, it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs, which have ample potential for reaping scale and scope benefits. © 2023, The Author(s).
Multi-step gH-difference-based methods for fuzzy differential equations
(Springer Nature, 2023) Safikhani, Leila; Vahidi, Alireza; Allahviranloo, Tofigh; Afshar Kermani, Mozhdeh
The main purpose of this paper is to introduce fuzzy Adams–Bashforth (A–B) and fuzzy Adams–Moulton (A–M) methods based on the generalized Hukuhara (gH)-differentiability and employ them as the predictor and corrector, respectively. The local truncation error, stability and convergence of these methods are discussed in the sequel. Finally, some fuzzy linear and nonlinear initial value problems (IVPs) are solved. The numerical results obtained here show that our methods provide a suitable approximation for the exact solution. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
Conditions to guarantee the existence of solutions for a nonlinear and implicit integro-differential equation with variable coefficients
(WILEY, 2022) Li, Chenkuan; Saadati, Reza; Allahviranloo, Tofigh
Using Babenko's approach, multivariate Mittag-Leffler (MM-L) function, and Krasnoselskii's fixed point theorem, we first investigate the existence of solutions to a Liouville-Caputo nonlinear integro-differential equation with variable coefficients and initial conditions in a Banach space. Then the existence of a positive solution for a variant equation is studied. Finally, we provide examples to illustrate the applications of the main results obtained.
The best approximation of generalized fuzzy numbers based on scaled metric
(HINDAWI LTD, 2022) Allahviranloo, Tofigh; Saneifard, Rasoul; Saneifard, Rahim; Kiani, Farzad; Noeiaghdam, Samad; Govindan, Vediyappan
The ongoing study has been vehemently allocated to propound an ameliorated alpha-weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using alpha-weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved.
Bifurcation and multiplicity of solutions of the navier-stokes equations in driven semi-elliptical cavity flow
(MDPI, 2022) Ertürk, Ercan; Allahviranloo, Tofigh
In this paper, bifurcations in the solution of the Navier-Stokes equations are studied and multiple solutions of the driven semi-elliptical cavity flow are presented. The two-dimensional steady incompressible driven viscous flow in a semi-elliptical cavity is solved numerically. To this end, the problem is formulated using an elliptic coordinate system that transforms the geometry conformally and provides a body fitted coordinate system. The presented results show that above a bifurcation Reynolds number the solution of the governing flow equations bifurcates and there exist multiple solutions for a particular Reynolds number when the aspect ratio of the semi-elliptical cavity geometry is 0.26 <= D <= 0.8. The bifurcation Reynolds numbers for different aspect ratios and also multiple solutions at different Reynolds numbers are presented in detail.
Z+-laplace transforms and Z+-differential equations of the arbitrary-order, theory and applications
(Elsevier Inc., 2022) Ardeshiri Lordejani, Maryam; Afshar Kermani, Mozhdeh; Allahviranloo, Tofigh
This paper provides a framework to study a class of arbitrary-order uncertain differential equations known as arbitrary-order Z+-differential equations. For this purpose, we first present the parametric form of Z+-numbers. Then, we introduce the basic algebraic operations on Z+-numbers, including addition, scalar multiplication, and Hukuhara difference. Definitely, these operations lead us to define the Z+-valued function. Afterward, the limit and continuity concepts of a Z+-valued function are provided under the definition of a metric on the space of Z+-numbers. Furthermore, the concepts of Z+-differentiability, Z+-integral, and Z+-Laplace transform with the convergence theorem for the Z+-valued function and its nth-order derivatives are introduced in detail. Considering all these concepts, a Z+-differential equation (Z+DE) can be expressed in the form of a bimodal differential equation combining a fuzzy initial value problem (FIVP) and a random differential equation (RDE). To this end, we use a combination of “FIVP under strongly generalized Hukuhara differentiability (SGH-differentiability)” and “random differential equation under mean-square differentiability (ms-differentiability)” to define the nth-order differential equations with Z+-number initial values. Further, the existence and uniqueness of the Z+-differential equations are examined by presenting several theorems. Finally, the effectiveness of the approaches is illustrated by solving two examples.
Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces
(SPRINGER HEIDELBERG, 2022) Eidinejad, Zahra; Saadati, Reza; Allahviranloo, Tofigh
In this paper, considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD). Our main goal is to investigate the existence of a unique solution for the presented system of NA-CNN-MD in the matrix-valued fuzzy spaces and using the fuzzy measure. After investigating the existence of a unique solution of NA-CNNs-MD which are rho-pseudo almost periodically, we prove the Mittag-Leffler stability and Mittag-Leffler attractiveness for rho-pseudo almost periodic functions. Finally, two examples are given to illustrate the theoretical results.
Modified grasshopper optimization algorithm optimized adaptive fuzzy lead-lag controller for coordinated design of FACTS controller with PSS
(IOS PRESS, 2022) Sahu, Preeti Ranjan; Hota, Prakash Kumar; Panda, Sidhartha; Long, Hoang Viet; Allahviranloo, Tofigh
This paper proposes adaptive fuzzy lead-lag controller structures for power system stabilizer and flexible AC transmission system based damping controllers to increase the stability of power system. The parameters of the proposed controller are tuned by a modified grasshopper optimization algorithm (MGOA). The new algorithm named MGOA accomplishes a proper balance between exploration and exploitation phases of original grasshopper optimization algorithm. This capability of MGOA is certified by using the benchmark functions by comparing with that of a grasshopper optimization algorithm, genetic algorithm, evolutionary strategies, particle swarm optimization, bat algorithm, population based incremental learning, flower pollination algorithm, monarch butterfly optimization and improved monarch butterfly optimization. The proposed controller is optimized and verified under various loading circumstances using MGOA method. The results of MGOA are compared with grasshopper optimization algorithm, genetic algorithm, and particle swarm optimization. Additionally, the results of the proposed MGOA are compared with conventional lead-lag controller to demonstrate its superiority.
Classical and intelligent methods in model extraction and stabilization of a dual-axis reaction wheel pendulum: a comparative study
(Elsevier B.V., 2022) Tavakol Aghaei, Vahid; Akbulut, Batuhan Ekin; Tan, Deniz; Allahviranloo, Tofigh; Fernandez Gamiz, Unai; Noeiaghdam, Samad; Bezci, Yüksel Ediz
Controlling underactuated open-loop unstable systems is challenging. In this study, first, both nonlinear and linear models of a dual-axis reaction wheel pendulum (DA-RWP) are extracted by employing Lagrangian equations which are based on energy methods. Then to control the system and stabilize the pendulum's angle in the upright position, fuzzy logic based controllers for both x ? y directions are developed. To show the efficiency of the designed intelligent controller, comparisons are made with its classical optimal control counterparts. In our simulations, as proof of the reliability and robustness of the fuzzy controller, two scenarios including noise-disturbance-free and noisy-disturbed situations are considered. The comparisons made between the classical and fuzzy-based controllers reveal the superiority of the proposed fuzzy logic controller, in terms of time response. The simulation results of our experiments in terms of both mathematical modeling and control can be deployed as a baseline for robotics and aerospace studies as developing walking humanoid robots and satellite attitude systems, respectively.
A solving method for two-dimensional homogeneous system of fuzzy fractional differential equations
(American Institute of Mathematical Sciences, 2022) Akram, Muhammad; Muhammad, Ghulam; Allahviranloo, Tofigh; Ali, Ghada
The purpose of this study is to extend and determine the analytical solution of a twodimensional homogeneous system of fuzzy linear fractional differential equations with the Caputo derivative of two independent fractional orders. We extract two possible solutions to the coupled system under the definition of strongly generalized H-differentiability, uncertain initial conditions and fuzzy constraint coefficients. These potential solutions are determined using the fuzzy Laplace transform. Furthermore, we extend the concept of fuzzy fractional calculus in terms of the MittagLeffler function involving triple series. In addition, several important concepts, facts, and relationships are derived and proved as property of boundedness. Finally, to grasp the considered approach, we solve a mathematical model of the diffusion process using proposed techniques to visualize and support theoretical results.
An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing
(Elsevier B.V., 2022) Ghalichi, Shabnam Sadat Seyed; Amirfakhrian, Majid; Allahviranloo, Tofigh
Some efficient radial basis functions (RBFs) have a free parameter called the shape parameter that controls the shape of approximating function. This parameter is mainly selected by trial and error related to the problem. Because of the significant role of this value in the accuracy and stability of the RBF method, we propose an algorithm to choose a good value as a shape parameter. In this work, we focus on the interpolating of scattered data approximation and attempt to find a better value of the shape parameter for RBF interpolation. The proposed algorithm selects a good value for the shape parameter by minimizing a cost function which imitates the error between the radial interpolant and the unknown function f that the data points sampled from the function f. The algorithm can be applied to a multidimensional problem of any dimension and for any radial basis function. Also, many experiments including interpolation of one and two dimensional data sets as well as zooming pictures consider investigating the efficiency of this procedure. Also, we show that this algorithm consistently finds a good value for a shape parameter ?.
Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator
(AMER INST MATHEMATICAL SCIENCES-AIMS, 2022) Akram, Muhammad; Ihsan, Tayyaba; Allahviranloo, Tofigh; Al-Shamiri, Mohammed M. Ali
This study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability). To this end, firstly the fourth-order derivative of the fuzzy valued function (FVF) according to the type of the SGH-differentiability is introduced, and then the relationships between the fourth-order derivative of the FVF and its Laplace transform are established. Furthermore, considering the types of differentiabilities and switching points, some fundamental theorems related to the Laplace transform of the fourth-order derivative of the FVF are stated and proved in detail and a method to solve FIVP by the fuzzy Laplace transform is presented in detail. An application of our proposed method in Resistance-Inductance circuit (RL circuit) is presented. Finally, FIVP's solution is graphically analyzed to visualize and support theoretical results.
Rational Groups whose character degree graphs are disconnected
(Academie des Sciences, 2022) Erkoç, Temha; Akar, Gamze
A finite group all of whose complex character values are rational is called a rational group. In this paper, we classify all rational groups whose character degree graphs are disconnected.
A variety of closed-form solutions, Painlevé analysis, and solitary wave profiles for modified KdV–Zakharov–Kuznetsov equation in (3+1)-dimensions
(Elsevier B.V., 2022) Nonlaopona, K.; Mann, N.; Kumar, S.; Rezaei, S.; Abdou, M.A.
The major goal of the article is to use the generalized exponential rational function method to seek abundant closed-form solutions and dynamics of solitary wave profiles to the (3+1)-dimensional modified KdV–Zakharov–Kuznetsov (MKdV–ZK) equation. We also apply the Painlevé analysis with Kruskal simplification to investigate the integrability of the said equation. The (3+1)-dimensional MKdV–ZK model is a significant model with great advantages in various disciplines of physics, such as nonlinear optics, fluid dynamics, plasma physics, mathematical physics, and quantum mechanics. By taking advantage of the generalized exponential rational function technique, we extracted various soliton solutions, including exponential form, trigonometric form, and hyperbolic form function solutions. From both mathematical and physical points of view, it is important to obtain bright–dark soliton forms and other solitonic wave profiles. Furthermore, the results have been graphically revealed using 3D, 2D, and contour plots to demonstrate the underlying dynamics of the interactive waves. The obtained findings indicate the method's efficacy and dependability, allowing it to be widely applied in a variety of advanced nonlinear evolution equations. © 2022 The Author(s)
Abundant solitary wave solutions to a perturbed Schrödinger equation with Kerr law nonlinearity via a novel approach
(Elsevier B.V., 2022) Aldhabani, M.S.; Nonlaopon, K.; Rezaei, S.; S.Bayones, F.; Elagan, S.K.; El-Marouf, S.A.A.
The main purpose of the present paper is to introduce a reliable method, for the first time, in solving differential equations with partial derivatives. The significant idea behind this method is the modification of a well-known method. The main base functions used in the solution's structures are Jacobi elliptic functions which are known functions and have many applications in practice. In order to achieve these results, the perturbed Schrödinger equation with Kerr law nonlinearity is considered. This nonlinear equation illustrates the propagation of optical solitons in nonlinear optical fibers. Thereupon, several analytical solutions corresponding to this model are obtained through employing an improved generalized exponential rational function method. Then we present a new version of it that is presented for the first time in the literature. Using these methods, several wave solutions related to the considered model are obtained. Moreover, several numerical simulations relevant to the resulting solutions are performed in the paper. As a notable features of the proposed method, the obtained solutions are characterized by the Jacobi elliptic functions. These solutions contain an index that for some specific choices is reduced to standard functions such as trigonometric and hyperbolic. The obtained results and solutions can be used for investigating the mechanism of several nonlinear phenomena laboratory and space plasmas. All necessary calculations are performed via symbolic packages of Wolfram Mathematica. © 2022 The Authors
The effects of a combination treatment with mesenchymal stem cell and platelet-rich plasma on tendon healing: an experimental study
(Turkiye Klinikleri, 2022) Uyar, İlker; Altuntaş, Zeynep; Fındık, Sıddıka; Yıldırım, Mehmet Emin Cem; Yarar, Serhat; Aktan, Murat; Avcı, Ahmet
Background/Aim: The objective of this study was to investigate the effects that the application of mesenchymal stem cells (MSCs) and platelet-rich plasma (PRP) following tendon repair have on the strength and healing of the tendon and also to examine the possible mechanisms of action that take place. Materials and methods: The Achilles tendons of 80 rats were repaired and divided into eight groups. Following the repairs, MSCs obtained from humans were injected into the rat tendons in groups 1 and 2, a combination of MSCs from humans and PRP from rats was injected into the tendons in groups 3 and 4, and PRP from rats was injected into the tendons in groups 5 and 6. These procedures all took place simultaneously. Groups 7 and 8 did not receive any injections following the repairs. The rats were sacrificed at the end of the first and second months following the procedures, and biomechanical and histopathological analyses were performed. Results: Inflammatory cell density increased most significantly in the combined group when compared to the first and second months. The fibroblast density on the tendon repair region was significantly lower in the second-months groups of each intervention compared to their first-month groups (p = 0.001). For the analysis of the maximum tensile breaking force, the behaviors of the groups over time were significant when compared to the control groups (p = 0.0015). Also, the mean maximum breaking force in the combined group was statistically significantly higher at the end of the second month than at the end of the first month (p = 0.0008). Conclusion: The combination therapy increased tendon strength force. This combination therapy can make a positive contribution to the healing of tendons after surgery. ©
Pyrolytic conversion of automotive bumper polywaste to diesel like fuel and its utilization in compression ignition engine
(Elsevier Ltd, 2022) Kiran, S.; Varuvel, Edwin Geo
In present scenario, alternate fuels for vehicle usage is aimed to satisfy the increasing energy demand significantly caused by fossil fuel depletion and global warming increase around the world. In today's world, plastics are the most indispensable material and their use in automobiles are increasing day by day. Many vehicles are scrapped year by year, from which plastic waste can be converted as usable fuel. This paper deals with analyzing the performance of diesel like fuel obtained by pyrolysis process from bumper waste and to study its emission and combustion behavior by using it in a compression ignition (CI) engine. For extraction, pyrolysis process was adopted and temperature was maintained at 240–360 °C. Fuel property testing was done on the resultant oil collected. It was then blended with diesel in the proportions of WBO P20, WBO P30, WBO P60, and WBO P80 with diesel and tested in a CI engine and its results analyzed. The results show WBO P20 is better with 31.43% BTE, 0.153% of CO emission, 1595 ppm of NO emission, 65.7% of smoke emission and 118 ppm of HC emissions slightly higher than diesel. The cylinder peak pressure for WBO P20 was found to be 71.08 bar and peak heat release was found to be 45.93 J/deg CA which matches diesel combustion. © 2022 Elsevier Ltd
On dynamics of an eco-epidemics system incorporating fractional operators of singular and nonsingular types
(Elsevier, 2022) Rezapour, S.; Rezaei, Somayeh; Khames, A.; Abdelgawad, M.A.; Ghoneim, M.M.; Riaz, M.B.
This paper examines three new definitions of the fractional derivative with singular and non-singular kernels in an eco-epidemics model of predator–prey type. The model describes the situation in which an infectious disease has been spread in the predator category that affects all other interactions in the system. Moreover, equilibrium points related to the model are identified and conditions related to the stability of each are stated. Further, several simulated scenarios have been provided to support the analytical discussions. The sensitivity of the models to changes in some parameters in them has been investigated and it was seen that these changes sometimes cause chaos in the studied dynamic systems. The utilized techniques in this contribution will enable us to handle other related eco-epidemics models including fractional-derivative operators in an accurate and efficient manner. © 2022 The Authors
Some novel approaches to analyze a nonlinear Schrodinger's equation with group velocity dispersion: Plasma bright solitons
(Elsevier, 2022) Rezaei, Somayeh; Rezapour, S.; Alzabut, J.; De Sousa, R.; Alotaibi, B.M.; El-Tantawy, S.A.
Taking two efficient analytical techniques, including the generalized exponential rational function method and the extended sinh–Gordon equation expansion method, into account several optical solutions to a variety of nonlinear Schrödinger's equation with group velocity dispersion are constructed. We are investigated several families of localized structures (bright solitons) for attractive nonlinearities including localized structures in both angular directions in addition to localized structures in one-directional and homogeneous in the other. To provide a better understanding of the obtained results, some numerical simulations for the obtained solutions are carried out. Further, the obtained solutions are represented graphically in order to clarify the vision and deep understanding of the mechanism of all nonlinear phenomena described by these solutions. The acquired results in this survey are new and have not been obtained in previous literature. Moreover, both utilized techniques can be assumed as an important tool for the explanation of some nonlinear physical phenomena such as the modulated envelope localized structures in plasma physics and fluid mechanics. Also, the obtained solutions can help researchers interested in studying the acoustic nonlinear modulated structures in different plasma models especially bright envelope solitons. © 2022 The Authors

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