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Yayın Matching of cocycle extensions for second tangent groups(American Institute of Physics Inc., 2022-11-07) Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, SerkanWe present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself.Yayın On matched pair Hamiltonian analysis of the compartmental models(Marmara Üniversitesi, 2020-10-30) Ateşli, Begüm; Esen, Oğul; Sütlü, Serkan; Yıldırım, KenanEpidemiological compartmental models predict the spread of an infectious disease that a specific population encounter. The population is divided into compartments representing different stages of the epidemic and the change of these compartments in time is given by nonlinear differential equations. In previous studies, the Hamiltonian analysis of these models is included. In this work, we briefly explain SIR, SEIR, 2-SIR and 2-SEIR models, and their Hamiltonian analysis. We recollect the matched pair Lie-Poisson systems and observe that SIR and SEIR models can be written as matched pair Lie-Poisson systems. We generalize the matched pair Lie-Poisson systems using the twisted cocycle extension. We attain that matched pair Lie-Poisson systems obtained by the twisted cocycle extension is convenient for 2-SIR and 2-SEIR models.Yayın Kinetic moments of Vlasov dynamics: a matched pair analysis(Marmara Üniversitesi, 2020-10-30) Esen, Oğul; Sütlü, Serkan; Yıldırım, KenanThis talk is based on [1]. We first present a gentle introduction to the Hamiltonian (Lie-Poisson) analysis of dynamical systems. Then we recast the dynamics of kinetic moments of Vlasov equation from the matched pair decomposition point of view. That is, we present the moment dynamics as a coupling of mutually interacting (Lie-Poisson) subdynamics. We observe that one of the constitutive subdynamics is the compressible isentropic fluid flow.Yayın On Lie groupoids, Lie algebroids and equations of motion under mutual actions(Marmara Üniversitesi, 2020-10-30) Esen, Oğul; Kaya, Hanife Kübra; Sütlü, Serkan; Yıldırım, KenanIn this work, we present matching of two mutually interacting Lagrangian systems on Lie algebroid frameworks. Firstly, we mention Lie groupoids and Lie algebroids formally. Due to the mutual actions of two Lie groupoids and two Lie algebroids onto each other, we refer the matched Lie groupoids and Lie algebroids structures. Then, we obtain Euler-Lagrange equations on the matched Lie algebroids which involve individual behaviours and mutual action terms. During this work, we provide many examples.
