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Yayın Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction(World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, SerkanWe 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.Yayın On the theory of single aspheric lenses(Institute of Electrical and Electronics Engineers Inc., 2024) Hasanoğlu, ElmanAspheric lenses play a pivotal role in a myriad of applications, including antenna theory, communication systems, sophisticated optical systems etc. These lenses, unlike their spherical counterparts, possess an infinite number of free parameters and by utilizing these parameters it is possible to achieve optical and antenna systems with very high and sophisticated performances. However, the lack of a rigorous mathematical theory essentially limits possibility to utilize their full potential in the related fields. In our days, the design process relies heavily on elementary mathematical principles and empirical methods [1-2]. Even a single thick aspheric lens lacks a comprehensive mathematical theory. In this paper a new mathematical approach to the theory of single lenses is proposed. Surprisingly, even in this seemingly straightforward case, the serious mathematical theory of a single aspherical lens relies on rather nontrivial mathematical principles as partial differential equations, differential geometry, Riemann geometry.
