Filtreler

2023 - 20255
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Ayarlar

Bölüm: Işık University, Faculty of Engineering and Natural Sciences, Department of Mathematics × Scopus Q: Q3 ×

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Listeleniyor 1 - 5 / 5
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    Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction
    (World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, Serkan
    We study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.
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    On Caputo fractional Bertrand curves in E3 and E31
    (Univ Nis, Fac Sci Math, 2024) Taşdemir, Mert; Canfes, Elif Özkara; Uzun, Banu
    In this article, we examine Bertrand curves in E3 and E31 by using the Caputo fractional derivative which we call alpha-Bertrand Curves. First, we consider alpha-Bertrand curves in E3 and we give a characterization of them. Then, we study alpha-Bertrand curves in E31 and we prove the necessary and sufficient condition for a alpha-Bertrand curves in E31 by considering time like, space like and null curves. We also give the related examples by using Python.
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    Harmonic resonance phenomena on nonlinear SH waves
    (Işık University Press, 2023-04) Ahmetolan, Semra; Özdemir, Neşe; Peker Dobie, Ayşe; Demirci, Ali
    The interaction of shear horizontal (SH) waves in a two layered elastic medium and its mth harmonic component is studied. The dispersion relation is analysed to obtain the wave number-phase velocity pairs where the third and fifth harmonic resonance phenomena emerge. By employing an asymptotic perturbation method it is shown that the balance between the weak nonlinearity and dispersion yields a coupled nonlinear Schrödinger (CNLS) equation for the slowly varying amplitudes of the fundamental wave and its fifth harmonic component. The nonlinearity effects of the materials and the ratio of layers’ thicknesses on the linear instabilities of solutions and the existence of solitary waves are examined.
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    Gluing formulas for volume forms on representation varieties of surfaces
    (Springer Nature, 2025-08-06) Erdal, Esma Dirican
    Let Σg,n be a compact oriented surface of genus g≥4 with n boundary components. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah–Bott–Goldman–Narasimhan symplectic form on the space of representations of π1(Σg,0) in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of Σg,0 in terms of torsions of Σg1,1,Σg2,1, and boundary circle S1, where g=g1+g2 and g1,g2≥2. Then, by using Heusener and Porti’s results on Σg,n, we show that the symplectic volume form on the representation variety of Σg,0 can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces Σg1,1 and Σg2,1.
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    Complex rays and applications
    (Işık University Press, 2025-12-01) Hasanoğlu, Elman
    Complex rays are a fascinating aspect of modern diffraction theory, typically sought as complex solutions to the eikonal equation. Traditionally, these solutions are obtained by analytically continuing real rays into the complex domain. However, this approach demands the analyticity of initial data, significantly limiting its applicability to many practical problems. Additionally, unlike real rays, complex rays cannot be visualized in space, presenting another drawback. In this paper, we present an alternative interpretation of complex rays, as introduced in [1], and describe a novel approach to two model diffraction problems and Gaussian beams.