Fen - Edebiyat Fakültesi
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Browsing Fen - Edebiyat Fakültesi by Department "Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü"
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Article A common fixed point theorem of a Gregus type on convex cone metric spaces(Eudoxus Press, 2011) Abdeljawad, Thabet; Karapınar, Erdal; 19184; MatematikThe result of Ciric [1] on a common fixed point theorem of Gregus-type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedralArticle A Kamenev-type oscillation result for a linear (1+alpha)-order fractional differential equation(Elsevier Science Inc., 2015) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal; MatematikWe investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1)Article A note on the chain rule on time scales(Çankaya Üniversitesi, 2008) Abdeljawad, Thabet; MatematikIt is known, in general, that the chain rule on general time scale derivatives does not behave well as in the case of usual derivative. However, we discuss some special cases where the time scale derivative has the usual chain rule. The results are analyzed for both the delta and nabla time scales derivatives.Article Asymptotic integration of (1+alpha)-order fractional differential equations(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; MatematikWe establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0.Article Checkerboard Julia sets for rational maps(World Scientific Publ., 2013) Çilingir, Figen; Çilingir, Figen; Cuzzocreo, Daniel; Devaney, Robert L.; Look, Daniel M.; Russell, Elizabeth D.; MatematikIn this paper, we consider the family of rational maps F-lambda(z) = z(n) + lambda/z(d), where n >= 2, d >= 1, and lambda is an element of C. We consider the case where lambda lies in the main cardioid of one of the n - 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps F-lambda and F-mu are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy mu = nu(j(d+1))lambda or mu = nu(j(d+1))(lambda) over bar where j is an element of Z and nu is an (n - 1)th root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.Article Chemometric Methods for the Simultaneous Spectrophotometric Determination of Telmisartan and Hydrochlorotiazide in the Commercial Pharmaceuticals(Chiminform Data S A, 2009) Baleanu, Dumitru; Dinç, Erdal; Baleanu, Dumitru; 6981; MatematikSimultaneous spectrophotometric determination of telmisartan (TEL) and hydrochlorothiazide (HCT) in two different commercial pharmaceutical preparations were performed by using three different chemometric methods, namely principal component regression (PCR), partial least squares (PLS) and artificial neural network (ANN). The proposed chemometric methods do not require chemical seperation and spectral graphical procedures for the quantitative resolution of mixtures containing the titled compounds. In the preparation of chemometric calibrations, a concentration set of 45 synthetic mixtures containing TEL and HCT in the linear concentration range of 1.0-26.0 and 1.0-17.0 mu g/mL, respectively was simetrically prepared in methanol. The spectra of the above concentration set and samples were recorded in the spectral range of 200-350 nm. Concentration set and its corresponding absorbances in the selected spectral range corresponding to the 250-350 nm wavelength range was used to obtain PCR, PLS and ANN calibrations. Recovery study, intra-day, inter-day and standard addition technique were considered as method validation. Three proposed chemometric approaches were sucessfully applied to the quantitative analysis of two different commercial pharmaceutical productsArticle Common fixed point theorems for generalized (phi,psi)-weak contraction condition in complete metric spaces(Springer, 2015) Taş, Kenan; Taş, Kenan; Patel, Uma Devi; 4971; MatematikThe intent of this manuscript is to establish some common fixed point theorems in a complete metric space under weak contraction condition for two pairs of discontinuous weak compatible maps. The results proved herein are the generalization of some recent results in literature. We give an example to support our resultsArticle Generalized (C)-conditions and related fixed point theorems(Pergamon-Elsevier Science Ltd, 2011) Karapınar, Erdal; Taş, Kenan; 19184; 42699; MatematikIn this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained.Article On a boundary value problem for a second order ODE(Çankaya Üniversitesi, 2008) Octavian, G. MustafaWe investigate the existence of solutions to a boundary value problem for a second order ordinary differential equation (ODE) over an unbounded interval. The conclusions are useful in studying certain reaction-diffusion equations via the comparison methodArticle On nonlinear fractional Klein-Gordon equation(Elsevier Science Bv, 2011) Baleanu, Dumitru; Golmankhaneh, Ali K.; Baleanu, Dumitru; MatematikNumerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equationArticle On the Non-Commutative Neutrix Product of the Distributions xλ + and xμ +(Springer Science & Business Media B.V., 2006) Taş, Kenan; Taş, Kenan; 4971; MatematikLet f and g be distributions and let gn = (g ∗ δn)(x), where δn(x) is a certain sequence converging to the Dirac delta function. The non-commutative neutrix product f ◦g of f and g is defined to be the limit of the sequence {fgn}, provided its limit h exists in the sense that N−lim n→∞ f(x)gn(x), ϕ(x) = h(x), ϕ(x) , for all functions ϕ in D. It is proved that (xλ + lnp x+) ◦ (xμ + lnq x+) = xλ+μ + lnp+q x+, (xλ − lnp x−) ◦ (xμ − lnq x−) = xλ+μ − lnp+q x−, for λ + μ < −1; λ, μ, λ + μ = −1, −2,... and p, q = 0, 1, 2.... .Article Some fixed point results for TAC-type contractive mappings(Hindawi Publishing Corporation, 2016) Taş, Kenan; Taş, Kenan; Ansari, Arslan Hojat; 4971; MatematikWe prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.Article The first integral method for the (3+1)-dimensional modified korteweg-de vries-zakharov-kuznetsov and hirota equations(Editura Academiei Romane, 2015) Baleanu, Dumitru; Kılıç, B.; Uğurlu, Y.; İnç, Mustafa; MatematikThe first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equationsArticle Vester's sensitivity model for genetic networks with time-discrete dynamics(Springer International Publishing, 2014) Defterli, Özlem; Defterli, Özlem; Fuegenschuh, Armin; Weber, Gerhard Wilhelm; MatematikWe propose a new method to explore the characteristics of genetic networks whose dynamics are described by a linear discrete dynamical model x(t+1) = Ax(t). The gene expression data x(t) is given for various time points and the matrix A of interactions among the genes is unknown. First we formulate and solve a parameter estimation problem by linear programming in order to obtain the entries of the matrix A. We then use ideas from Vester's Sensitivity Model, more precisely, the Impact Matrix, and the determination of the Systemic Roles, to understand the interactions among the genes and their role in the system. The method identifies prominent outliers, that is, the most active, reactive, buffering and critical genes in the network. Numerical examples for different datasets containing mRNA transcript levels during the cell cycle of budding yeast are presentedArticle Yüzey terimleri ve jenerik-olmayan simetriler(Çankaya Üniversitesi, 2004) Baleanu, Dumitru; MatematikKilling-Yano tensörleri, eğimli manifoldlarda süpersimetrik klasik ve quvantum mekaniğiyle derinden ilişkilidir. Bu makalede bir serbest parçacık Lagrange’ına yüzey terimleri ekleyen kare Lagrange terimleri ortaya konmuştur. Kare Lagrange terimleri tarafından oluşturulan manifold yapısına karşılık gelen Killing-Yano tensörleri hesaplanmış ve ilgili jenerik olmayan simetriler gösterilmiştir.
