A new approach for the sequence spaces of fuzzy level sets with the partial metric

In this paper, we investigate the classical sets of sequences of fuzzy numbers by using partial metric which is based on a partial ordering. Some elementary notions and concepts for partial metric and fuzzy level sets are given. In addition, several necessary and sufficient conditions for partial completeness are established by means of fuzzy level sets. Finally, we give some illustrative examples and present some results between fuzzy and partial metric spaces

Analysis of the properties of the solutions of a thin domain problem under periodic boundary conditions

Bu tezde, akışkanlar dinamiğinin temel denklemlerinden olan Navier-Stokes denklemleri ile ısı denkleminden oluşan Rayleigh-Bénard konveksiyonu, Boussinesq yaklaşımı altında ele alınmıştır. Düzgün bir fonksiyon tarafından sınırlanan bir ince bölge üzerinde denklem sisteminin zayıf ve güçlü çözümlerinin varlığı ve tekliği Galerkin yöntemi kullanılarak gösterilmiştir. Denklem sisteminin çözümlerinin asimptotik davranışlarını incelemek üzere belirleyici değerlerinin sayısı üzerinde bir üst sınır elde edilmiş, yerel olmayan çekicilerin varlığı gösterilmiştir. Yerel olmayan çekici üzerinde yer alan güçlü çözümler için veri ekleme analizi yapılmıştır. Ayrıca, denklemin parametrelere olan sürekli bağlılığı belirli şartlar altında gösterilmiştir.In this thesis, the Rayleigh-Bénard convection equations, which is comprised of Navier-Stokes equations and a heat equation, is discussed under the Boussinesq approximation. The existence and uniqueness of the weak and strong solutions of the equation system on a thin domain prescribed by a uniform function is proved by using the Galerkin method. In order to examine the asymptotic behavior of the solutions of the equation system, upper bounds on the number of determining modes were obtained and the existence of the global attractor is shown. The data assimilation alghorithm is examined for the strong solutions in the global attractor. In addition, the continuous dependence of the solutions on the parameters is shown under certain conditions

Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus

Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions