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In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Bu çalışmada, Boole yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal kavramı tanımlanmıştır. Elde edilen yeni tanımla birlikte Boole idealler ile literatürdeki diğer yapılar arasındaki ilişkiler incelenmiştir. Her Boole idealin aynı zamanda bir IFP ideal olduğu ancak tersinin doğru olmadığı ispatlanmıştır. Yine, Boole yakın halkaların sıfırlayan ideallerinin de Boole ideal olduğu ispatlanmıştır. Ayrıca, kendisi Boole olmadığı halde Boole ideale sahip çeşitli yakın halkalar örnek olarak incelenmiştir. Son olarak, verilen bir Boole halkadan Boole yakın halka elde etme yöntemi ile bir Boole yakın halka elde edilmiştir.

The Covid-19 pandemic has brought a lot of concerns about the operational and financial situation of businesses. Forecasting is crucial as it guides businesses through these critical points. Forecasting has become even more critical in the pandemic environment and therefore the necessity of using an accurate forecasting method has increased. Taking this into consideration, in this study, intelligent machine learning methods, namely; Grey Model (GM), Artificial Neural Network (ANN) and Support Vector Machine (SVM) are applied to make a short-term prediction of a food supplement, a product whose demand increased with the pandemic situation. Eighty-five percent of the historical data is used for training purposes and fifteen percent of the data is used for measuring accuracy. The accuracy of the models employed is improved with parameter optimization The accuracy performance indicator Mean Absolute Percentage Error (MAPE) showed that all methods give superior results when the historical data has an increasing sales trend. This study presents an important consideration for businesses and has a potential to be generalized for a business whose sales have an increasing trend not only because of the pandemic but also for any reason.

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