Communications, Series A1:Mathematics and Statistics

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    A new family of the continuous distributions: the extended Weibull-G family
    (Ankara Üniversitesi, 2019-02-01) Korkmaz, Mustafa Çagataş; Other; Other
    In this study, we present a new family of continuous distributions via an extended form of the Weibull distribution. Some special members of the newly defined family are discussed and the new univariate continuous distributions are introduced. The mathematical properties are obtained for any members of the family such as expansions of the density, hazard rate function, quantile function, moments and order statistics. We obtain the distribution parameters by maximum likelihood method. The simulation study to evaluate the performance of the estimated parameters based on the selected member of the this new family is also given. The lifetime data example is discussed to illustrate the applicability of the distribution.
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    Classical Way of Looking at the Lane-Emden Equation
    (Ankara Üniversitesi, 2019-02-01) Tanrıverdi, Tanfer; Other; Other
    In this article, the well-known approximate and analytical solutions of the Lane-Emden equation applying Taylor series expansion are derived. To the best of author's knowledge nobody has overcome the singularity of the Lane-Emden equation at the origin as it is carried out here
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    Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Yıldırım, Ümit; Atçeken, Mehmet; Dirik, Süleyman; Other; Other
    In the present paper we have studied the curvature tensor of a normal paracontact metric manifold satisfying the conditions R(ξ,X)P=0, P(ξ,X)R=0, P(ξ,X)P=0, P(ξ,X)S=0, P(ξ,X)Z=0 and pseudo projective flatness, where R, P, S and Z denote the Riemannian curvature, pseudo projective curvature, Ricci and concircular curvature tensors, respectively.
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    Smarandache Curves in three dimensional Lie groups
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Değirmen, Caner; Okuyucu, O. Zeki; Yıldız, Ö. Gökmen; Other; Other
    In this paper, we introduce special Smarandache curves and obtain Frenet apparatus of a Smarandache curve in three dimensional Lie groups with a bi-invariant metric. Moreover, we give some relations between a helix or a slant helix curve and its Smarandache curve in three dimensional Lie groups.
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    A Generalized Version of Foster and Stuart's d-statistic
    (Ankara Üniversitesi, 2019-02-01) Tanıl, Halil; Other; Other
    Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in. In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation. The exact and asymptotic distributions of the proposed test statistic are obtained for a random continuous sequence which is independent and identically distributed (i.i.d.). Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.
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    Some new d-orthogonal polynomial sets of Sheffer type
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Varma, Serhan; Matematik; Fen Fakültesi
    In this paper, we present some new Sheffer type d-orthogonal polynomial sets. Moreover, we obtain the d-dimensional functional vector ensuring the d-orthogonality of these new polynomial sets.
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    On Complex Modified Genuine Szász-Durrmeyer-Stancu Operators
    (Ankara Üniversitesi, 2019-02-01) Çetin, Nursel; Other; Other
    In this paper, we introduce complex modified genuine Szász-Durrmeyer-Stancu operators to improve the results obtained in [4] and present overconvergence properties of these operators. We obtain some estimates on the rate of convergence, a Voronovskaja-type result and the exact order of approximation for these operators attached to analytic functions of exponential growth on compact disks.
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    Quasi-Sasakian Structures on 5-dimensional Nilpotent Lie Algebras
    (Ankara Üniversitesi, 2019-02-01) Özdemir, Nilüfer; Aktay, Şirin; Solgun, Mehmet; Other; Other
    In this study, we examine the existence of quasi-Sasakian structures on nilpotent Lie algebras of dimension five. In addition, we give some results about left invariant quasi-Sasakian structures on Lie groups of dimension five, whose Lie algebras are nilpotent. Moreover, subclasses of quasi-Sasakian structures are studied for some certain classes.
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    Approximately Groups in Proximal Relator Spaces
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) İnan, Ebubekir; Other; Other
    The focus of this article is on defining descriptive approximations of sets or algebraic structures in proximal relator spaces. By way of a practical application, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with descriptive Efremovic proximity relations are introduced.
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    Mathematical Analysis and Numerical Simulations for the Cancer Tissue Invasion Model
    (Ankara Üniversitesi, 2019-02-01) Meral, Gülnihal; Yamanlar, İbrahim Çağatay; Other; Other
    Cancer cell invasion is one of the most important stages of metastasis. In this paper, the local existence and uniqueness of the cancer cell invasion model is proved using an iterative procedure. Moreover the numerical simulations are performed using a combination of a nonstandard finite difference scheme and backward and forward Euler methods. It is seen that the results agree well with the expected behaviour of the invasion.
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    Coefficient estimates for bi-concave functions
    (Ankara Üniversitesi, 2019-02-01) Sakar, F. Müge; Güney, H. Özlem; Other; Other
    In this study,a new class C_{Σ}^{p,q}(α) of analytic and bi-concave functions were presented in the open unit disc. The coefficients estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| were found for functions belonging to this class.
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    Eigenvalues and scattering properties of difference operators with impulsive condition
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Erdal, İbrahim; Yardımcı, Şeyhmus; Matematik; Fen Fakültesi
    In this work, we are concerned with difference operator of second order with impulsive condition. By the help of a transfer matrix M, we present scattering function of corresponding operator and examine the spectral properties of this impulsive problem.
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    k-autocorrelation and its applications
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Özimamoğlu, Hayrullah; Şahin, Murat; Ölmez, Oktay; Matematik; Fen Fakültesi
    The standard autocorrelation measures similarities between a binary sequence and its any shifted form. In this paper, we introduce the concept of the k-autocorrelation of a binary sequence as a generalization of the standard autocorrelation. We give two applications of the k-autocorrelation. The first one is related the additive circulant codes over F₄ in coding theory. We use the k-autocorrelation to determine the minimum distance of additive circulant codes over F₄. The second one is related the (7,3,1)-BIBD in design theory. The k-autocorrelation coefficients give us information about the lines in the (7,3,1)-BIBD.
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    Quasi 2-absorbing second modules
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Ansari-Toroghy, H.; Farshadifar, F.; Other; Other
    In this paper, we will introduce the notion of quasi 2-absorbing second modules over a commutative ring and obtain some basic properties of this class of modules.
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    Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution
    (Ankara Üniversitesi, 2019-02-01) Özdemir, Şenay; Güney, Yeşim; Tuaç, Yetkin; Arslan, Olcay; İstatistik; Fen Fakültesi
    Marshall--Olkin extended Burr XII (MOEBXII) distribution is proposed by Al-Saiari et al. (2014) to obtain a more flexible family of distributions. Some estimation methods like maximum likelihood, Bayes and M estimations are used to estimate the parameters of the MOEBXII distribution in literature. In this paper, we propose to use Maximum Lq (MLq) estimation method to find alternative estimators for the parameters of the MOEBXII distribution. We give some simulation studies and a real data example to compare the performance of the MLq estimators with the maximum likelihood and M estimators. According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.
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    Smarandache Curves According to Sabban Frame Belonging to Mannheim Curves Pair
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Şenyurt, Süleyman; Altun, Yasin; Cevahir, Ceyda; Other; Other
    In this paper, we investigate special Smarandache curves according to Sabban frame, using the idea of Mannheim partner curve of spherical indicatrix. We created Sabban frame by means of Mannheim partner curve of spherical indicatrix. We explained that position vectors of a Smarandache curves are consisted by Sabban frame given above. Then we calculated geodesic curvatures of this Smarandache curve and the results which we found after calculations are expressed by means of Mannheim partner curve of spherical indicatrix.
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    On the spectrum and Hilbert Schimidt properties of generalized Rhaly matrices
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) MURSALEEN, Mohammad; YİLDİRİM, Mustafa; DURNA, Nuh; Other; Other
    In this paper, we show that the multiplications of some generalized Rhaly operators are Hilbert Schimidt operators.We also calculate the spectrum and essential spectrum of a special generalized Rhaly matrices on the Hardy space H².
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    On two times differentiable preinvex and prequasiinvex functions
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) İşcan, İmdat; Kadakal, Mahir; Kadakal, Huriye; Other; Other
    The main goal of this paper is to establish a new identity for functions defined on an open invex subset of real numbers. By using this identity, the Hölder integral inequality and power mean integral inequality, we introduce some new type integral inequalities for functions whose powers of second derivatives in absolute values are preinvex and prequasiinvex.
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    On the linear codes over the ring Z₄+v₁Z₄+...+v_{t}Z₄
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Dertli, Abdullah; Cengellenmiş, Yasemin; Other; Other
    Some results on linear codes over the ring Z₄+uZ₄+vZ₄,u²=u,v²=v,uv=vu=0 in [6,7] are generalized to the ring D_{t}=Z₄+v₁Z₄+...+v_{t}Z₄,v_{i}²=v_{i},v_{i}v_{j}=v_{j}v_{i}=0 for i≠j,1≤i,j≤t. A Gray map Φ_{t} from D_{t}ⁿ to Z₄^{(t+1)n} is defined. The Gray images of the cyclic, constacyclic and quasi-cyclic codes over D_{t} are determined. The cyclic DNA codes over D_{t} are introduced. The binary images of them are determined. The nontrivial automorphism on D_{i} for i=2,3,...,t is given. The skew cyclic, skew constacyclic and skew quasi-cyclic codes over D_{t} are introduced. The Gray images of them are determined. The skew cyclic DNA codes over D_{t} are introduced. Moreover, some properties of MDS codes over D_{t} are discussed.