Asimptotik davranış, ters problem, ek integral şartı, parabolik ve pseudo-parabolik denklem. Son yıllarda matematiksel fizik alanında önemli mesafeler katedilmiştir. Özellikle de fiziksel olayların matematik modellemesi üzerine kaydadeğer çalışmalar yapılmıştır. Bunlardan biri de iyi konulmamış (ill-posed) problemler sınıfından olan ters problemler üzerine yapılan çalışmalardır. Bu çalışmalarda daha çok ters problemlerin çözümünün varlığı-tekliği ve çözümlerin uzun zaman davranışı araştırılmıştır. Bu çalışmada ters problemler için varlık teklik probleminden ziyade -çünkü bu alanda pek çok çalışma yapılmıştır- üzerinde pek çalışılmamış olan parabolik ve pseudo- parabolik denklemler için ters problemlerin çözümünün asimptotik davranışı araştırıldı. İlk bölümde ters problemlerle ilgili bu zamana kadar yapılan çalışmalar anlatıldı. Daha sonra fonksiyon uzayları ve bazı temel eşitsizlikler verildi. İkinci bölümde doğrusal parabolik denklemler için direkt problem ifade edildikten sonra direkt problemin çözümünün varlığı-tekliği araştırıldı. Problemin çözümü ile ilgili bazı kestirimler elde edildi. Üçüncü bölümde parabolik ve pseudo-parabolik denklemler için ters problemler ifade edildi ve ters problemlerin çözümünün varlığı-tekliği araştırıldı. Dördüncü bölümde, parabolik ve pseudo-parabolik denklemler için ters problemlerin çözümünün asimptotik davranışı araştırıldı, ikinci mertebeden, dördüncü mertebeden ve yüksek mertebeden parabolik denklemler için bazı varsayımlar altında ek integral şartı ile verilen ters problemlerin çözümünün t -» +qo asimptotik davranışı hakkında bazı sonuçlar elde edildi.
THE EFFECT OF ADDITIVE MATERIALS ON STRUCTURE AND PROPERTIES IN POLYMER MATRIX COMPOSITES SUMMARY Keywords: Polypropylene), red mud, polymer matrix composite material, environmental protection, injection moulding, mechanical, thermal and physical properties In this study, thermoplastic matrix composites and their properties were investigated. Poly(propylene) (matrix material) and red mud (filler/reinforced material) were used in production of polymer matrix composite material. In this investigation, poly(propylene) and red mud were firstly mixed to produce composite material that had different red mud compositions. Injection molding was choosen as our manufacturing process. Composite materials that were composed of five different (% 10-20-30-40-50) red mud ratio were produced. Second, some experimental tests such as grain size distribution, tensile, bending, hardness, density, water absorption and freezing resistance testing were applied. In addition, for thermal characterization, TG (Thermo-gravimetric), DTA (Differential Thermal Analysis), DSC (Differential Scanning Calorimetry), and physical characterization XRD (X-Ray Diffraction), EDAX (Energy Dispersive X-Ray Analysis), XRF (X-Ray Fluorescence Spectroscopy), Gamma-Ray Spectroscopy and SEM (Scanning Electron Microscope) techniques were used. The average grain size of the red mud is approximately 37 um. Tensile strength, bending strength and percent of elongation of produced composite material were decreased with red mud addition. The values of hardness and density were increased with increasing of red mud ratio. Water absorption rate and freezing lost of measured in freezing resistance testing of composite material were increased with increasing of red mud ratio. TG/DTA analysis performed at atmospheric condition showed that, the firing temperature of the composite was increased with increasing of filler material ratio. The result of the DSC analysis showed increment both in melting enthalpy and the ratio of crystallinity. XRD analysis showed change of crystal orientation of poly(propylene). Elemental analysis of red mud was carried out with the EDAX and XRF techniques. EDAX and XRF analysis showed the existence of major Na, Al, Si, S, K, Ca, Ti and Fe, besides these elements, some elements like Cr, Ni, Sr, Y and Zr as minor quantities were detected. ^Th232'04 and ^u238'03 gamma radioactivity of the red mud were measured as 539±18 Bq/kg and 218±9 Bq/kg, respectively. The quantity of the Th calculated from 90xn232'04 activity was found as 119±3 gTh/tone Red mud, ^u238'03 was 1,58±0,45 gTh/tone Red mud. With SEM studies, the microstructure of composite was investigated and existence of agglomerate particles were detected as several small red mud sub particles. The manufacturing studies of composite materials was made in PLASCAM Co. Most part of the tests and examinations were carried out at Department of Metallurgical and Materials Engineering in our university and The Department of The Polymer Science and Engineering Laboratories of The Materials Science Centre/UMIST in University of Manchester. XXI
