Cilt:71 Sayı:04 (2022)
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Item Study and suppression of singularities in wave-type evolution equations on non-convex domains with cracks(Ankara Üniversitesi, 2022) Seck, Cheikh; Other; OtherOne of the objectives of this paper is to establish the exact controllability for wave-type evolution equations on non-convex and/or cracked domains with non-concurrent support crack lines. Admittedly, we know that according to the work of Grisvard P., in domains with corners or cracks, the formulas of integrations by parts are subject to geometric conditions: the lines of cracks or their supports must be concurrent. In this paper, we have established the exact controllability for the wave equation in a domain with cracks without these additional geometric conditions.Item A study on modeling of rat tumours with the discrete-time Gompertz model(Ankara Üniversitesi, 2022) Özbek, Levent; İstatistik; Fen FakültesiCancer formation is one of the pathologies whose frequency has increased in the recent years. In the literature, the compartment models, which are non-linear, are used for such problems. In nonlinear compartment models, nonlinear state space models and the extended Kalman filter (EKF) are used to estimate the parameter and the state vector. This paper presents a discrete-time Gompertz model (DTGM) for the transfer of optical contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. The DTGM, which is proposed for ICG and the estimation of ICG densities used in the vascular invasion of tumor cells of the compartments and in the measurement of migration from the intravascular area to the tissues, is obtained from the experimental data of the study. The ICG values are estimated online (recursive) using the DTGM and the adaptive Kalman filter (AKF) based on the experimental data. By employing the data, the results show that the DTGM in conjunction with the AKF provides a good analysis tool for modeling the ICG in terms of mean square error (MSE), mean absolute percentage error (MAPE), and . When the results obtained from the compartment model used in the reference [9] are compared with the results obtained with the DTGM, the DTGM gives better results in terms of MSE, MAPE and R 2 criteria. The DTGM and the AKF compartment model require less numerical processing when compared to the EKF, which indicates that DTGM is a less complicated model. In the literature, EKF is used for such problems.Item Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators(Ankara Üniversitesi, 2022) Kara, Mustafa; Other; OtherIn the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.Item Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators(Ankara Üniversitesi, 2022) Kara, Mustafa; Other; OtherIn the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.Item Dual numbers, topology, dual analytic functions(Ankara Üniversitesi, 2022) Akgül, Arzu; Other; OtherIn geometric function theory, Lucas polynomials and other special polynomials have recently gained importance. In this study, we develop a new family of bi-univalent functions. Also we examined coefficient inequalities and Fekete-Szegö problem for this new family via these polynomials.Item An overview to analyticity of dual functions(Ankara Üniversitesi, 2022) Aktaş, Burak; Other; OtherIn this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail. Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on D n . Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.Item Spectral singularities of an impulsive Sturm-Liouville operators(Ankara Üniversitesi, 2022) Öznur, Güler Başak; Other; OtherIn this paper, we handle an impulsive Sturm–Liouville equation with complex potential on the semi axis. The objective of this work is to examine some spectral properties of this impulsive Sturm–Liouville equation. By the help of a transfer matrix B, we obtain Jost solution of this problem. Furthermore, using Jost solution, we find Green function and resolvent operator of this equation. Finally, we consider two unperturbated impulsive Sturm–Liouville operators. We examine the eigenvalues and spectral singularities of these problems.Item Approximation properties of Bernstein's singular integrals in variable exponent Lebesgue spaces on the real axis(Ankara Üniversitesi, 2022) Akgün, Ramazan; Other; OtherIn generalized Lebesgue spaces L p ( . ) with variable exponent p ( . ) defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals in these spaces are obtained. Estimates of simultaneous approximation by integral functions of finite degree in L p ( . ) are proved.Item Some results on pseudosymmetric normal paracontact metric manifolds(Ankara Üniversitesi, 2022) Mert, Tuğba; Other; OtherIn this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For normal paracontact metric manifolds, pseudosymmetric cases are investigated and some interesting results are obtained. We show that a semisymmetric normal paracontact manifold is of constant sectional curvature. We also obtain that a pseudosymmetric normal paracontact metric manifold is an η -Einstein manifold. Finally, we support our topic with an example.Item Farey graph and rational fixed points of the extended modular group(Ankara Üniversitesi, 2022) Demir, Bilal; Other; OtherFixed points of matrices have many applications in various areas of science and mathematics. Extended modular group ¯¯¯¯ Γ is the group of 2 × 2 matrices with integer entries and determinant ± 1 . There are strong connections between extended modular group, continued fractions and Farey graph. Farey graph is a graph with vertex set ^ Q = Q ∪ { ∞ } . In this study, we consider the elements in ¯¯¯¯ Γ that fix rationals. For a given rational number, we use its Farey neighbours to obtain the matrix representation of the element in ¯¯¯¯ Γ that fixes the given rational. Then we express such elements as words in terms of generators using the relations between the Farey graph and continued fractions. Finally we give the new block reduced form of these words which all blocks have Fibonacci numbers entries.Item Parity of an odd dominating set(Ankara Üniversitesi, 2022) Batal, Mehmet; Other; OtherFor a simple graph G with vertex set V ( G ) = { v 1 , . . . , v n } , we define the closed neighborhood set of a vertex u as \\ N [ u ] = { v ∈ V ( G ) | v is adjacent to u or v = u } and the closed neighborhood matrix N ( G ) as the matrix whose i th column is the characteristic vector of N [ v i ] . We say a set S is odd dominating if N [ u ] ∩ S is odd for all u ∈ V ( G ) . We prove that the parity of the cardinality of an odd dominating set of G is equal to the parity of the rank of G , where rank of G is defined as the dimension of the column space of N ( G ) . Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.Item Chen invariants for Riemannian submersions and their applications(Ankara Üniversitesi, 2022) Gülbahar, Mehmet; Other; OtherIn this paper, an optimal inequality involving the delta curvature is exposed. With the help of this inequality some characterizations about the vertical motion and the horizontal divergence are obtained.Item Set-generated soft subrings of rings(Ankara Üniversitesi, 2022) Kamacı, Hüseyin; Other; OtherThis paper focuses on the set-oriented operations and set-oriented algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties of α -intersection of soft set are investigated, where α is a non-empty subset of the universal set. Later, by using α -intersection of soft set, the notion of set-generated soft subring of a ring is introduced. The generators of soft intersections and products of soft subrings are given. Some related properties about generators of soft subrings are investigated and illustrated by several examples.Item On the zeros of R-Bonacci polynomials and their derivatives(Ankara Üniversitesi, 2022) Özgür, Nihal; Other; OtherThe purpose of the present paper is to examine the zeros of R-Bonacci polynomials and their derivatives. We obtain new characterizations for the zeros of these polynomials. Our results generalize the ones obtained for the special case r=2. Furthermore, we find explicit formulas of the roots of derivatives of R-Bonacci polynomials in some special cases. Our formulas are substantially simple and useful.Item On F -cosmall morphisms(Ankara Üniversitesi, 2022) Tütüncü, Derya Sezgin; Other; OtherIn this paper, we first define the notion of F -cosmall quotient for an additive exact substructure F of an exact structure E in an additive category A . We show that every F -cosmall quotient is right minimal in some cases. We also give the definition of F -superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure F .Item Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers(Ankara Üniversitesi, 2022) Durmaz, Muhammet Enes; Other; OtherThe work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.Item Ideal convergence of a sequence of Chebyshev radii of sets(Ankara Üniversitesi, 2022) Albayrak, Hüseyin; Other; OtherIn this paper, we investigate the diameters, Chebyshev radii, Chebyshev self-radii and inner radii of a sequence of sets in the normed spaces. We prove that if a sequence of sets is I -Hausdorff convergent to a set, the sequence of Chebyshev radii of that sequence is I-convergent. Similar relations are showed for the sequence of diameters, Chebyshev self-radii and inner radii of that sequence.Item Dominator semi strong color partition in graphs(Ankara Üniversitesi, 2022) SUNDARESWARAN, Raman; Other; OtherLet G =(V,E) be a simple graph. A subset S is said to be Semi-Strong if for every vertex v in V, |N(v)∩S|≤1, or no two vertices of S have the same neighbour in V, that is, no two vertices of S are joined by a path of length two in V. The minimum cardinality of a semi-strong partition of G is called the semi-strong chromatic number of G and is denoted by χsG. A proper colour partition is called a dominator colour partition if every vertex dominates some colour class, that is , every vertex is adjacent with every element of some colour class. In this paper, instead of proper colour partition, semi-strong colour partition is considered and every vertex is adjacent to some class of the semi-strong colour partition.Several interesting results are obtained.Item Sharp weak bounds for p-adic Hardy operators on p-adic linear spaces(Ankara Üniversitesi, 2022) Gürbüz, Ferid; Other; OtherThe current paper establishes the sharp weak bounds of p-adic fractional Hardy operator. Furthermore, optimal weak type estimates for p-adic Hardy operator on central Morrey space are also acquired.Item Local T 0 and T 1 quantale-valued preordered spaces(Ankara Üniversitesi, 2022) Özkan, Samed; Other; OtherIn this paper, we characterize explicitly the separation properties T 0 and T 1 at a point p in the topological category of quantale-valued preordered spaces and investigate how these characterizations are related. Moreover, we prove that local T 0 and T 1 quantale-valued preordered spaces are hereditary and productive.