TR-Dizin
Permanent URI for this collectionhttps://ada.atilim.edu.tr/handle/123456789/21
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Browsing TR-Dizin by Scopus Q "Q2"
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Article Citation Count: 0A convergent two-level linear scheme for the generalized Rosenau–KdV–RLW equation(Tubitak Scientific & Technological Research Council Turkey, 2019) Aydın, Ayhan; Aydın, Ayhan; MathematicsA new convergent two-level finite difference scheme is proposed for the numerical solution of initial valueproblem of the generalized Rosenau–KdV–RLW equation. The new scheme is second-order, linear, conservative, andunconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solutionis studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence ofthe scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating thesolitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically.Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term.Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulatesthe solitary waves for a long time.Article Citation Count: 0Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)(Tubitak Scientific & Technological Research Council Turkey, 2021) Aydın, Ayhan; Köroğlu, Canan; Aydın, Ayhan; MathematicsIn this paper, we consider the Burgers equation B(2, 2) . Exact and nonstandard finite difference schemes(NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equationB(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. Thesetwo NSFD schemes are compared with a standard finite difference (SFD) scheme. Numerical results show that the NSFDschemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We seethat although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results forlong time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.Article Citation Count: 0Fedja’s proof of Deepti’s inequality(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet; Turan, Mehmet; Ostrovska, Sofiya; MathematicsThe paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.Editorial Citation Count: 0Introduction: Marxifying IR, IRifying Marxism(International Relations Council of Turkey, 2024) Yalvaç,F.; Yalvaç, Faruk; Joseph,J.; International RelationsAlthough the neglect of Marxism has been a pervasive characteristic of IR theory, there has been a marked revival of interest in Marxism. Marx’s materialist insights into the general historical development of societies, as well as his critique of capitalism and political economy, have served as alternative starting points for different critical approaches to IR and offers a welcome alternative to neorealism, constructivism, and poststructuralism that have dominated IR for several decades. Marxism provides a redefinition of IR by focusing on changes in material circumstances, historical conditions, and society instead of assuming unchanging and fixed structures of anarchy or the state. Marx’s analysis and insights into the dynamics of international relations have become even more important given the ongoing crisis of neoliberal capitalism, the rise of authoritarianism, right-wing nationalist populisms, and the racial and gendered subordinations accompanying them pointing to the importance of Marxifying IR and IRifying Marxism. © 2024, International Relations Council of Turkey. All rights reserved.Article Citation Count: 0Number fields and divisible groups via model theory(Tubitak Scientific & Technological Research Council Turkey, 2021) CELIK, Sermin C. A. M.; GORAL, HaydarIn this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.Article Citation Count: 3On strongly autinertial groups(Tubitak Scientific & Technological Research Council Turkey, 2018) Onur, Cansu Betin; MathematicsA subgroup X of G is said to be inert under automorphisms (autinert) if |X : $X^\\alpha$ ∩ X| is finite for allα ∈ Aut(G) and it is called strongly autinert if | < X, $X^\\alpha$ >: X| is finite for all α ∈ Aut(G). A group is calledstrongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. Wecharacterize such groups for a finitely generated case. Namely, we prove that a finitely generated group G is stronglyautinertial if and only if one of the following hold:i) G is finite;ii) G = ⟨a⟩ ⋉ F where F is a finite subgroup of G and ⟨a⟩ is a torsion-free subgroup of G.Moreover, in the preliminary part, we give basic results on strongly autinert subgroups.Article Citation Count: 1A short note on some arithmetical properties of the integer part of ap(Tubitak Scientific & Technological Research Council Turkey, 2019) Akbal, Yıldırım; MathematicsLet $a>0$ be an irrational number. We study some of the arithmetical properties of ${\\{\\lfloor ap\\rfloor\\}}_{p=2}^\\infty$ where pdenotes a prime number and $\\lfloor x\\rfloor$ denotes the largest integer not exceeding x.Article Citation Count: 0Some permutations and complete permutation polynomials over finite fields(Tubitak Scientific & Technological Research Council Turkey, 2019) Gülmez Temür, Burcu; Temür, Burcu Gülmez; MathematicsIn this paper we determine $b\\in F_{q^n}^\\ast$ for which the polynomial $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a permutationpolynomial and determine $b\\in F_{q^n}^\\ast$ for which the polynominal $f(x)=x^{s+1}+bx\\in F_{q^n}\\left[x\\right]$ is a complete permutationpolynomial where $s=\\frac{q^n-1}t,\\;t\\in\\mathbb{Z}^+$ such that $\\left.t\\;\\right|\\;q^n-1$.Article Citation Count: 0Strategic Hedging or Alignment? Qatar’s Foreign Policy Toward Iran in the Wake of the Blockade Crisis(Uluslararasi Iliskiler Konseyi dernegi, 2023) Orhan, Duygu Dersan; Orhan, Duygu Dersan; International RelationsThe blockade imposed on Qatar changed the power dynamics in the Persian Gulf, increasing tension and insecurity in the area. Qatar’s ability to overcome the blockade was largely due to its cooperation with Iran, and the two countries’ ties grew as a result. This study investigates whether Qatar’s long-standing hedging toward Iran has changed into an alignment in the wake of the 2017 blockade. The key conclusion of the article is that, despite Qatar’s faint signals of alignment with Iran during the blockade, it did not entirely stray from its hedging strategy. Qatar-Iran relations has been selected as a case study to illustrate the effects of regional developments and security crises on the hedging strategy within the context of the Blockade Crisis.