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Öğe Entropy Solution of a First Order Hyperbolic Type Equations with a Non-Convex State Function in a Class Of Discontinuous Functions(Beykent Üniversitesi, 2012) Resulov, Mahir; Sahin, Ethem IlhanIn this paper, a method for obtaining an exact and numerical solution of the Cauchy and first type initial boundary value problems for a first order partial differential equation with a non convex state function is suggested. For this purpose, we introduce an auxiliary problem since it has some advantages over the main problem, and it is equivalent to the main problem in a definite sense. Using this auxiliary problem, we propose a efficient method for finding the location of shock which appears in the solution of main problem and its evolution in time. The suggested auxiliary problem permit also us to prove of convergence in mean of a numerical solution to the exact solution of the main problem. Moreover, using the auxiliary problem we can write the higher order numerical scheme with respect to the time variable. Some results of the comparison of the exact and numerical solutions are illustrated.Öğe Structural and dielectric performance of the Ba(Zn1/3Nb2/3-xSbx)O3 perovskite ceramics(Iop Publishing Ltd, 2019) Qasrawi, A. F.; Sahin, Ethem Ilhan; Emek, Mehriban; Kartal, Mesut; Kargin, SerdarIn this work, we have explored the antimony doping effects on the structural and dielectric properties of Ba(Zn1/3Nb2/3)O-3 ceramics (BZN). The ceramics displayed perovskite structures with a lattice constant that decreases with increasing Sb content. The antimony solubility limit of the BZN ceramics is x < 0.50. Belowthis limit and in the range of 0.30 <= x <= 0.40, the microstrain, the dislocation density and the stacking faults decreased and the crystallite size increases with increasing Sb content in the composition of BZN. When the limit is exceeded minor phases are predicted by software analysis and confirmed by the experimental techniques. The presence of these phases is also verified by the scanning electron microscopy and energy dispersive x-ray spectroscopy techniques. Increasing the Sb content is observed to decrease the value of the dielectric constant. The Sb doped BZN ceramics exhibits high dielectric quality factors that nominate it for applications in electronics as radio waves resonators.