Matematik Bölümü Makale Koleksiyonu

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

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Interior Schauder-type estimates for m - th order elliptic operators in rearrangement-invariant Sobolev spaces
(Tubitak scientific & technological research council Turkey, 2024) Mamedov, Eminağa M.; Çetin, Şeyma
In this study, we investigate the m-th order elliptic operators on n-dimensional bounded domain ohm subset of R n with discontinuous coefficients in the rearrangement-invariant Sobolev space W X m (ohm). In general, the considered rearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantial modification of classical methods and a lot of preparation, concerning correctness of substitution operator, problems related to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of these spaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on the shift operator. We establish interior Schauder-type estimates in the above subspaces. Note that Lebesgue spaces L p (ohm), grand-Lebesgue spaces, Marcinkiewicz spaces, weak-type L w p spaces, etc. are also covered by such spaces.
New concept of centrality measurement in fuzzy social networks
(IOS Press BV, 2024) Mahapatra, Rupkumar; Samanta, Sovan; Pal, Madhumangal
The most critical task of a social network is to identify a central node. Numerous methods for determining centrality are documented in the literature. It contributes to online commerce by disseminating news, advertisements and other content via central nodes. Existing methods capture the node's direct reachability. This study introduces a novel method for quantifying centrality in a fuzzy environment. This measurement takes into account the reachability of nodes and their direct connections. Several critical properties have been demonstrated. A small Facebook network is used to illustrate the issue. Additionally, appropriate tables and graphs present a comparative study with existing methods for centrality measurement. © 2024-IOS Press. All rights reserved.
Reconstruction of old maps based on old photos using fuzzy graphs
(Springer, 2024) Borzooei, Rajab Ali; Shadravan, M.; Takallo, M. Mohseni; Allahviranloo, Tofigh
About 70 years ago, the reconstruction conjecture was proposed as an interesting problem in graph theory. In this paper, we extend the concept of reconstruction to fuzzy graphs and introduce the new concept of recognizable properties. We then explore various recognizable properties of fuzzy graphs, including regularity, degree sequence, strength, and block. Additionally, we identify some reconstructable fuzzy graphs. Finally, in conclusion, the reconstruction of fuzzy graphs can be applied to recover old maps by analyzing old photos.
Topology on CL-algebras
(Springer science and business media deutschland GmbH, 2024) Khajeh Nasir H.; Aaly Kologani M.; Borzooei, Rajab Ali
In this paper, by considering the notion of L-algebras and CL-algebras, we construct a topology on a bounded CL-algebra. Then, we investigate some of its topological properties, such as Hausdorff space, T0-space and T1-space and connectedness. Moreover, we express the relation between closed and compact sets in this topology. Finally, by considering the notion of semi-topological algebra, we prove that any commutative bounded CL-algebra is a right semi-topological algebra.
Density results on hyperharmonic integers
(Mathematical Society of Japan, 2025) Sertbaş, Doğa Can
It was conjectured that there are no hyperharmonic integers h(nr) except 1. In 2020, a disproof of this conjecture was given by showing the existence of infinitely many hyperharmonic integers. However, the corresponding proof does not give any general density results related to hyperharmonic integers. In this paper, we first get better error estimates for the counting function of the pairs (n, r) that correspond to non-integer hyperharmonic numbers using sums on gaps between consecutive prime numbers. Then, based on a plausible assumption on prime powers with restricted digits, we show that there exist positive integers n such that the set of positive integers r where h(nr) ∈ Z has positive density. Apart from that, we also obtain exact densities of sets {r ∈ Z>0: h(33r) ∈ Z} and {r ∈ Z>0: h(39r) ∈ Z}. Finally, we give the smallest hyperharmonic integer h(nr) greater than 1, which is obtained when n = 33 and r = 10 667 968. ©2025 The Mathematical Society of Japan.
A note on variants of Euler's φ-function
(Institute of Mathematics, University of Debrecen, 2024) Büyükaşık, Engin; Göral, Haydar; Sertbaş, Doğa Can
It is well-known that the sum of the first n consecutive integers always divides the k-th power sum of the first n consecutive integers when k is odd. Motivated by this result, in this note, we study the divisibility properties of the power sum of positive integers that are coprime to n and not surpassing n. First, we prove a finiteness result for our divisibility sets using smooth numbers in short intervals. Then, we find the exact structure of a certain divisibility set that contains the orders of these power sums and our result is of computational flavour. © 2024 Institute of Mathematics, University of Debrecen. All rights reser
Advances in sand cat swarm optimization: a comprehensive study
(Springer science and business media B.V., 2025) Anka, Ferzat; Aghayev, Nazim
This study provides an in-depth review and analysis of the nature-inspired Sand Cat Swarm Optimization (SCSO) algorithm. The SCSO algorithm effectively focuses on exploring solution areas inspired by sand cat hearing and finding the most suitable solutions for their hunting behavior. This algorithm is easily adaptable to various problems due to its stability, low-cost, flexibility, simple implementation, simplicity, derivative-free mechanism, and reasonable computation time. For these reasons, although it was published recently, it has begun to attract the attention of researchers. SCSO-based research has been presented in prestigious international journals such as Elsevier, Springer, MDPI, and IEEE since its inception in 2022. The studies cited in this paper are examined in three categories: improved, hybrid, and adapted. Research trends show that 39, 21, and 40% of SCSO-based studies fall into these three categories, respectively. Additionally, research on solving various problems inspired by the SCSO algorithm is discussed from two different perspectives: global optimizations and real-world applications. Analysis of the applications shows that 15 and 85% of the studies belong to these two fields, respectively.
FUZZY SUB-EQUALITY ALGEBRAS BASED ON FUZZY POINTS
(Lodz University, 2024) Aaly Kologani, Mona; Mohseni Takallo, Mohammad; Bae Jun, Young; Borzooei, Rajab Ali
In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈ ∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α, β)-fuzzy subalgebras and (α, β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset. © Copyright by Author(s), Lódź 2023 © Copyright for this edition by the University of Lodz, Lódź 2023.
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 ?.

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