Abstract. In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form F = (α + β) 2 /α, where α = q a i j y i y j is a Riemannian metric and β = b i y i is a 1-form. Then we completely determine the local structure of those with constant flag curvature.

In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form F = (α + β) 2 /α, where α = q a i j y i y j is a Riemannian metric and β = b i y i is a 1-form. Then we completely determine the local structure of those with constant flag curvature.

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey-predator model are examined. These models are solved numerically by Pell-Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell-Lucas series. By utilizing Pell-Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell-Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different (N, M) values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems.

ÖZETBu çalışmanın amacı, İzmir ilinin Seferihisar ilçesinde bulunan, belirli yaş aralığındaki 235 öğrencinin dmft/DMFT indekslerinin, yaş, cinsiyet, beslenme, oral hijyen alışkanlıkları, sosyal durum gibi farklı parametrelerle olan ilişkisini değerlendirmektir. Öğrenciler, 8-12 ve 13-16 yaş gruplarında olmak üzere 2 grupta incelendi. Gerekli verilerin elde edilmesi ve öğrencilerin sosyal alışkanlıklarının belirlenebilmesi amacı ile bireylere anket uygulandı. Ağız muayeneleri ise, gün ışığında ayna ve sond yardımıyla yapıldı. Elde edilen veriler Kruskal-Wallis, Mann-Whitney U ve Kikare testleri kullanılarak hesaplandı. Yapılan değerlendirmeler sonunda 8-12 yaş grubunda ortalama DMFT değeri 1,01, 13-16 yaş grubunda ise 1,27 bulundu. 8-12 yaş grubu dmft değeri ortalama 2,88 olarak hesaplandı. Cinsiyet, ana ve ara öğün sayısı, evde uygulanan koruyucu tedavi yöntemlerinin ve dişhekimine gitme sıklığının dmft/DMFT değerleri üzerinde anlamlı bir etkisi görülmezken, 8-12 yaş grubu öğrencilerin dmft indeksinin yaş ve diş fırçalama sıklığı parametrelerinden etkilendiği gözlendi. Bu grup çocuklarda yaş arttıkça dmft değerinin azaldığı saptandı.Toplumların tedavi gereksinimlerinin belirlenmesindeki en önemli veriler olan dmft ve DMFT indekslerinin hesaplanması, beslenme, oral hijyen alışkanlıkları, ağız diş sağlığı bilinç düzeyi gibi parametrelerin tespiti ve bu yönde yapılan çalışmalar, ağız diş sağlığı düzeylerinin yükselmesine katkıda bulunabilir. Anahtar kelimeler: ağız diş sağlığı, diş çürüğü, DMFT indeksi ABSTRACTThe aim of this study is to evaluate the relationship between dmft/DMFT index and various parameters such as age, gender, diet, oral hygiene habits, sociobehavioral status of 235 students in particular age groups. Students, ages between 8-12 and 13-16, have been recruited for this study. Questionnaire method was used to collect the requested data and determine the social habits of the students. The examination was carried out using intra-oral mirror and a probe in day light. Kruskal-Wallis, Mann Whitney U and Chi square tests were used to analyze the data. The mean DMFT score was found to be 1,01 for ages between 8-12 and 1,27 for ages between13-16. Whereas for age range of 8-12, the dmft value came out to be 2.88. The results revealed that there were no correlation between DMFT scores and gender, number of meals and snacks, home use of preventive oral care products and frequency of dentists visits. However it was observed that the dmft score for 8-12 years has been affected by age and frequency of toothbrushing. In addition as the age of the students increased the dmft score was found to be lower in this particular group. As a conclusion, determination of dmft/DMFT indicies, dietary and oral hygiene habits, level of dental consciousness for communities and abundance of researches to this effect may help to improve oral health status of society. Key words: oral dental health, dental caries, DMFT index

In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higher order linear Fredholm-Volterra integro differential equations (FVIDE). The approximate solutions are assumed in form of the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, the solution form and its derivatives are brought to matrix forms. By applying the collocation method based on equally spaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of this system determines the coefficients of assumed solution. Error estimation is made and also a method with the help of the obtained approximate solution is developed that finds approximate solution with better results. Then, the applications are made on five examples to show that the method is successful. In addition, the results are supported by tables and graphs and the comparisons are made with other methods available in the literature. All calculations in this study have been made using codes written in Matlab.