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    Boundedness in a parabolic-elliptic chemotaxis system with logistic source involving the exponents depending on the spatial variables and nonlinear signal productions
    (Taylor & Francis Ltd, 2025) Ayazoglu, Rabil; Simsek, Ramazan
    This paper considers the global boundedness of solutions to the parabolic-elliptic chemotaxis system with a logistic source involving exponents that depend on spatial variables and nonlinear signal production: {u(t) = u-chi del . (u del upsilon) + u (eta - mu u(alpha(x))) , (x, t) is an element of Omega x (0, T), 0 = upsilon - upsilon + u sigma, (x, t) is an element of Omega x (0, T), where eta >= 0, mu, sigma > 0, and alpha : Omega -> (0, infinity) is a measurable function, subject to the homogeneous Neumann boundary conditions in a if either sigma < max {ess inf(x is an element of Omega) alpha (x) , 2 bounded domain R-N (N >= 1) with smooth boundary. We prove that }, chi > 0 or ess inf(x is an element of Omega) alpha (x) < N sigma chi>0 or sigma=essinfx is an element of Omega alpha(x)>= (2)/(N) with mu > (N sigma -2)/ (N sigma) chi, chi > 0 or chi<0, then the above system possesses a unique global bounded classical solution.
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    Some harmonic problems on the tangent bundle with a berger-type deformed sasaki metric
    (Politechnica University of Bucharest, 2020) Altunbas, Murat; Simsek, Ramazan; Gezer, Aydin
    Let (M2k, ?, g) be an almost anti-paraHermitian manifold and (T M, gBS) be its tangent bundle with a Berger type deformed Sasaki metric gBS . In this paper, we deal with the harmonicity of the canonical projection ?: T M ? M and a vector field ? which is considered as a map ?: M ? T M. © 2020, Politechnica University of Bucharest. All rights reserved.
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    SOME HARMONIC PROBLEMS ON THE TANGENT BUNDLE WITH A BERGER-TYPE DEFORMED SASAKI METRIC
    (Univ Politehnica Bucharest, Sci Bull, 2020) Altunbas, Murat; Simsek, Ramazan; Gezer, Aydin
    Let (M-2k, phi, g) be an almost anti-paraHermitian manifold and (TM, g(BS)) be its tangent bundle with a Berger type deformed Sasaki metric g(BS). In this paper, we deal with the harmonicity of the canonical projection pi : TM -> M and a vector field xi which is considered as a map xi : M -> TM.
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    A Study Concerning Berger Type Deformed Sasaki Metric on the Tangent Bundle
    (B Verkin Inst Low Temperature Physics & Engineering, 2019) Altunbas, Murat; Simsek, Ramazan; Gezer, Aydin
    Let TM be the tangent bundle over an almost anti-paraHermitian manifold endowed with Berger type deformed Sasaki metric g B s. In this paper, first, we obtain the Levi-Civita connection of this metric and study geodesics on TM. Secondly, we construct some almost anti-paraHermitian structures on TM and search conditions for these structures to be anti-paraKahler and quasi-anti-paraKahler. Finally, we present certain Riemannian curvature properties of (TM, g(BS)).