WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Conference Object Killing-Yano Tensors, Surface Terms and Superintegrable Systems(Amer inst Physics, 2004) Baleanu, Dumitru; Baleanu, D; Defterli, Ö; Defterli, Özlem; MatematikKilling-Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2-sphere of unit radius and we analyze the symmetries of the obtained geometries.Conference Object Compatibility of Non-Generic Supersymmetries and Geometric Duality for a Subclass of Generalized Pp-Wave Metrics(Amer inst Physics, 2004) Baleanu, D; Baleanu, Dumitru; Baskal, S; MatematikSpinning point particle theories accommodate non-generic supercharges in connection with the existence of Killing-Yano tensors. Killing-Yano tensors of order two and three and their corresponding Killing tensors are found for a subclass of generalized pp-wave metrics. These metrics include the pp-wave itself, its possible generalizations and the Siklos metric which is conformal to that. The compatibility between geometric duality and non-generic symmetries is discussed within the context of the metric solutions. It is found that some of the metric solutions admit anti-de Sitter spacetimes while some are found to be purely radiative.Conference Object Citation - WoS: 2Fractional Euler-Lagrange Equations for Constrained Systems(Amer inst Physics, 2004) Avkar, Tansel; Avkar, T; Baleanu, D; Baleanu, Dumitru; MatematikThe fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n-fold integration and integer-order differentiation. Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler-Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler-Lagrange equations are obtained, and the recovery of the classical results is discussed.Conference Object Differential Algebraic Equations in Primal Dual Interior Point Optimization Methods(Amer inst Physics, 2004) Kasap, S; Kasap, Suat; Trafalis, TB; Endüstri MühendisliğiPrimal dual Interior Point Methods (IPMs) generate points that lie in the neighborhood of the central trajectory. The key ingredient of the primal dual IPMs is the parameterization of the central trajectory. A new approach to the parameterization of the central trajectory is presented. Instead of parameterizing the central trajectory by the barrier parameter, it is parameterized by the time by describing a continuous dynamical system. Specifically, a new update rule based on the solution of an ordinary differential equation for the barrier parameter of the primal dual IPMs is presented. The resulting ordinary differential equation combined with the first order Karush-Kuhn-Tucker (KKT) conditions, which are algebraic equations, are called differential algebraic equations (DAEs). By solving DAEs, we find an optimal solution to the given problem.Conference Object Oscillation Criteria for Second Order Impulsive Delay Differential Equation(Amer inst Physics, 2004) Taş, Kenan; Alzabut, J; Zafert, A; Baleanu, Dumitru; MatematikA necessary and sufficient condition is obtained for oscillation of bounded solutions of second order impulsive delay differential equations of the form (r(t)x(t))'+p(t)f(x(i(t)))=0, t not equal theta Delta(r(theta(i))x'(theta(i)))+b(i)g(x(sigma(theta(i)))) = 0, i is an element of Z, Deltax(theta(i)) = 0. An example is also inserted to illustrate the effect of impulses on the oscillatory behavior of the solutions.Conference Object Citation - WoS: 2Citation - Scopus: 2Difference Discrete Variational Principles(Amer inst Physics, 2006) Baleanu, Dumitru; Jarad, FahdThe paper provides the discrete Lagrangian and Hamiltonian formulations of mechanical systems for both non-singular and singular cases. The Lagrangians with linear velocities and with higher velocities are investigated and the corresponding difference Euler-Lagrange equations and Hamiltonians are found.Conference Object An Overview of Mean Field Theory in Combinatorial Optimization Problems(Amer inst Physics, 2004) Kasap, S; Trafalis, TBIn the last three decades, there has been significant interest in using mean field theory of statistical physics for combinatorial optimization. This has led to the development of powerful optimization techniques such as neural networks (NNs), simulated annealing (SA), and mean field annealing (MFA). MFA replaces the stochastic nature of SA with a set of deterministic equations named as mean field equations. The mean field equations depend on the energy function of the NNs and are solved at each temperature during the annealing process of SA. MFA advances to the optimal solution in a fundamentally different way than stochastic methods. The use of mean field techniques for the combinatorial optimization problems are reviewed in this study.Conference Object Citation - WoS: 1Citation - Scopus: 1Fmml: a Feature Model Markup Language(Amer inst Physics, 2011) Nabdel, Leili; Karatas, Ahmet Serkan; Oguztuzun, Halit; Dogru, AliFeature modeling is a common way of representing commonality and variability in Software Product Line Engineering. Alternative notations are available to represent feature models. Compared with graphical notations, text-based notations can be more amenable to automated processing and tool interoperability. In this paper, we propose an XML-based feature modeling language to represent extended feature models with complex relationships.Conference Object Reproducing Kernel Method for Strongly Non-Linear Equation(Amer inst Physics, 2018) Akgul, Esra Karatas; Baleanu, Dumitru; Akgul, AliIn this paper, we search the efficiency of the reproducing kernel method (RKM) in solving the strongly nonlinear equation. An example is presented to prove the power of the technique. The results attained from the technique are compared with the other techniques. Results prove that the presented technique is very effective.Conference Object Citation - WoS: 2Citation - Scopus: 1Invariant Investigation on the System of Hirota-Satsuma Coupled Kdv Equation(Amer inst Physics, 2018) Balmeh, Z.; Akgul, A.; Akgul, E. K.; Baleanu, D.; Hashemi, M. S.We show how invariant subspace method can be extended to the system time fractional differential equations and construct their exact solutions. Effectiveness of the method has been illustrated by the time fractional Hirota-Satsuma Coupled KdV(HSCKdV) equation.