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Öğe A New Method for the Sum-Edge Characteristic Polynomials of Graphs(Boletim da Sociedade Paranaense de Matematica, 2022) Öz, Mert Sinan; Cangul, Ismail NaciIn this paper, the determinant of the sum-edge adjacency matrix of any given graph without loops is calculated by means of an algebraic method using spanning elementary subgraphs and also the coefficients of the corresponding sum-edge characteristic polynomial are determined by means of the elementary subgraphs. Also, we provide a formula for calculating the number of smallest odd-sized cycles in a given regular graph.Öğe Directed topological complexity of spheres(Springer Nature, 2020) Borat, Ayşe; Grant, MarkWe show that the directed topological complexity [as defined by Goubault (On directed homotopy equivalences and a notion of directed topological complexity, 2017. arXiv:1709.05702)] of the directed n-sphere is 2, for all n≥ 1. © 2019, The Author(s).Öğe NOTES ON THE SECOND-ORDER TANGENT BUNDLES WITH THE DEFORMED SASAKI METRIC(Ankara Üniversitesi, 2021) Karaca, Kübra; Gezer, Aydın; Mağden, AbdullahThe paper deals with the second-order tangent bundle (TM)-M-2 with the deformed Sasaki metric (g) over bar over an n-dimensional Riemannian manifold (M, g). We calculate all Riemannian curvature tensor fields of the deformed Sasaki metric (g) over bar and search Einstein property of (TM)-M-2. Also the weakly symmetry properties of the deformed Sasaki metric are presented.Öğe A New Type of F-Contraction and Their Best Proximity Point Results with Homotopy Application(SPRINGER, 2022) Şahin, HakanIn the present paper, we aim to extend and unify the results obtained for the multivalued F-contractions, which have been frequently studied recently, in a different way from the results in the literature without using the Pompeiu-Hausdorff metric. Hence, we first introduce a new class of multivalued mappings that includes multivalued F-contractions. Then, we obtain some best proximity point results for new kind of F-contraction mappings. Thus, we unify and improve many results in the literature. To see this fact, we give some nontrivial and interesting examples. Also, considering the strong relationship between homotopy theory and various branches of mathematics, we obtain an application to homotopy theory of our main result.Öğe On Rings whose Quasi Projective Modules Are Projective or Semisimple(RGN Publication, 2021) Ertaş, Nil Orhan; Acar, UmmahanFor two modules M and N, P-M(N) stands for the largest submodule of N relative to which M is projective. For any module M, P-M(N) defines a left exact preradical. It is given some properties of P-M(N). We express P-M(N) as a trace submodule. In this paper, we study rings with no quasi-projective modules other than semisimples and projectives, that is, rings whose quasi-projectives are either projective or semisimple (namely QPS-ring). Semi-Artinian rings and rings with no right p-middle class are characterized by using this functor: a ring R right semi-Artinian if and only if for any right R -module M, P-M(M) <=(e) M.Öğe On Almost Projective Modules(MDPI, 2021) Ertaş, Nil OrhanIn this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if M is generalized N-projective for any modules M and N, then M is almost N-projective. We also show that if M is almost N-projective and N is lifting, then M is im-small N-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting.Öğe Computing the Hosoya and the Merrifield-Simmons Indices of Two Special Benzenoid Systems(University of Kashan, 2021) Öz, Mert Sinan; Cangul, Ismail NaciGutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems Rn and Pn. In this paper, we compute the Hosoya index and Merrifield-Simmons index of Rn and Pn by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of Rn and Pn by means of a product of a certain matrix of degree n and a certain vector.Öğe Inverse scattering problem for linear system of four-wave interaction problem with equal number of incident and scattered waves(Birkhauser, 2021) Ismailov, Mansur I.; Tekin, İbrahimThe first order semi-strict hyperbolic system on the semi-axis in the case of equal number of incident and scattered waves are considered. The uniqueness of the inverse scattering problem (the problem of finding the potential with respect to scattering operator) is studied by utilizing it to Gelfand–Levitan–Marchenko type linear integral equations. It is determined the sufficient quantity of scattering problems (on the semi-axis for the same hyperbolic system) for ensuring the uniqueness of the inverse scattering problem.Öğe Inverse problem for the time-fractional euler-bernoulli beam equation(VGTU, 2021) Tekin, İbrahim; Yang, HeIn this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.Öğe Higher homotopic distance(Juliusz Schauder Center for Nonlinear Analysis, 2021) Borat, Ayşe; Vergili T.The concept of the homotopic distance and its higher analogs are introduced in [7]. In this paper we introduce some important properties of higher homotopic distances, investigate the conditions under which cat, secat and higher dimensional topological complexity categories are equal to the higher homotopic distance, and give alternative proofs, using higher homotopic distances, to some TCn-related theorems.Öğe Determination of a time-dependent coefficient in a non-linear hyperbolic equation with non-classical boundary condition(Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2021) Tekin, İbrahimThe non-linear hyperbolic equation is used to model many non-linear phenomena. In this paper, we consider an initial boundary value problem for non-linear hyperbolic equation. We determine a time-dependent coefficient multiplying non-linear term by using an additional condition, and prove the existence and uniqueness theorem for small times. We also propose a numerical scheme to solve the inverse problem for non-linear hyperbolic equation, and give test examples for sine, quadratic and cubic non-linearity.Öğe Digital homotopic distance between digital functions(Universidad Politecnica de Valencia, 2021) Borat, AyşeIn this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as being digitally homotopy invariance.Öğe Computing the Merrifield-Simmons indices of benzenoid chains and double benzenoid chains(Springer Science and Business Media Deutschland GmbH, 2021) Öz, Mert Sinan; Cangul I.N.In this paper, we introduce the Merrifield-Simmons vector defined at a path of corresponding double hexagonal (benzenoid) chain. By utilizing this vector, we present reduction formulae to compute the Merrifield-Simmons index σ(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute σ(H) of H by means of a product of some of obtained six matrices and a vector with entries in N. Subsequently, we introduce the simple Merrifield-Simmons vector defined at an edge of given graph G. By using simple Merrifield-Simmons vector we present reduction formulae to compute the σ(G) where G represents any hexagonal (benzenoid) chain.Öğe A randomized greedy algorithm for piecewise linear motion planning(MDPI, 2021) Ortiz C.; Lara A.; González J.; Borat, AyşeWe describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle R, and outputs an explicit system of piecewise linear motion planners for R. The algorithm is designed in such a way that the cardinality of the output is probabilistically close (with parameters chosen by the user) to the minimal possible cardinality.This yields the first automated solution for robust-to-noise robot motion planning in terms of simplicial complexity (SC) techniques, a discretization of Farber’s topological complexity TC. Besides its relevance toward technological applications, our work reveals that, unlike other discrete approaches to TC, the SC model can recast Farber’s invariant without having to introduce costly subdivisions. We develop and implement our algorithm by actually discretizing Macías-Virgós and Mosquera-Lois’ notion of homotopic distance, thus encompassing computer estimations of other sectional category invariants as well, such as the Lusternik-Schnirelmann category of polyhedra.Öğe An Inverse Problem for the Forced Transverse Vibration of a Rectangular Membrane with Time Dependent Potential(2020) Tekin, İbrahimIn this paper, an initial-boundary value problem for a two-dimensional waveequation which arises in the equation of motion for the forced transverse vibration of a rectangular membrane is considered. Giving an additional condition, a time-dependentcoefficient is determined and existence anduniqueness theorem for smalltimes is proved.Moreover, characterization of the conditional stability isgivenand numerical solution of the inverse probleminvestigatedby using finite difference method.Öğe On almost α-para-Kenmotsu manifolds satisfyıng certain conditions(2019) Küpeli Erken, İremIn this paper, we study some remarkable properties of almost ?- para-Kenmotsu manifolds. We consider pro jectively áat, conformally áat and concircularly áat almost ?-para-Kenmotsu manifolds (with the ?-parallel tensor Öeld ?h). Finally, we present an example to verify our results.Öğe Digital Lusternik–Schnirelmann category(2018) Borat, Ayşe; Vergili, TaneIn this paper, we define the digital Lusternik–Schnirelmann category cat? , introduce some of its properties, and discuss how the adjacency relation affects the digital Lusternik–Schnirelmann categoryÖğe A Generalized Wintgen Inequality for Legendrian Submanifolds in Almost Kenmotsu Statistical Manifolds(2019) Görünüş, Ruken; Erken, İrem Küpeli; Yazla, Aziz; Murathan, CengizhanMain interest of the present paper is to obtain the generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu statistical manifolds.Öğe A Neutral relation between metallic structure and almost quadratic ϕ-structure(2019) Gönül, Sinem; Erken, İrem Küpeli; Yayla, Aziz; Murathan, CengizhanIn this paper, we give a neutral relation between metallic structure and almost quadratic metric ?-structure. Considering N as a metallic Riemannian manifold, we show that the warped product manifold R ?f N has an almost quadratic metric ?-structure. We define Kenmotsu quadratic metric manifolds, which include cosymplectic quadratic manifolds when $\beta=0$. Then we give nice almost quadratic metric ?-structure examples. In the last section, we construct a quadratic ?-structure on the hypersurface $M^n$ of a locally metallic Riemannian manifold $M^{n+1}$Öğe Digital Lusternik-Schnirelmann category of digital functions(2020) Vergili, Tane; Borat, AyşeRoughly speaking, the digital Lusternik-Schnirelmann category of digital images studies how far a digital image is away from being digitally contractible. The digital LusternikSchnirelmann category (digital LS category, for short) is defined in [A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish J. Math. 2018]. In this paper, we introduce the digital LS category of digital functions. We will give some basic properties and discuss how this new concept will behave if we change the adjacency relation in the domain and in the image of the digital function and discuss its relation with the digital LS category of a digital image.
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