Akgül, İsmail

In convolutional neural networks, pooling methods are used to reduce both the size of the data and the number of parameters after the convolution of the models. These methods reduce the computational amount of convolutional neural networks, making the neural network more efficient. Maximum pooling, average pooling, and minimum pooling methods are generally used in convolutional neural networks. However, these pooling methods are not suitable for all datasets used in neural network applications. In this study, a new pooling approach to the literature is proposed to increase the efficiency and success rates of convolutional neural networks. This method, which we call MAM (Maximum Average Minimum) pooling, is more interactive than other traditional maximum pooling, average pooling, and minimum pooling methods and reduces data loss by calculating the more appropriate pixel value. The proposed MAM pooling method increases the performance of the neural network by calculating the optimal value during the training of convolutional neural networks. To determine the success accuracy of the proposed MAM pooling method and compare it with other traditional pooling methods, training was carried out on the LeNet-5 model using CIFAR-10, CIFAR-100, and MNIST datasets. According to the results obtained, the proposed MAM pooling method performed better than the maximum pooling, average pooling, and minimum pooling methods in all pool sizes on three different datasets.

Çakmak, Ali; Kiziltuǧ, Sezai; Mumcu, Gökhan

In this paper, we define the curve rλ= r + λd at a constant distance from the edge of regression on a curve r(s) with arc length parameter s in Galilean 3-space. Here, d is a non-isotropic or isotropic vector defined as a vector tightly fastened to Frenet trihedron of the curve r(s) in 3-dimensional Galilean space. We build the Frenet frame {Tλ,Nλ,Bλ} of the constructed curve rλwith respect to two types of the vector d and we indicate the properties related to the curvatures of the curve rλ. Also, for the curve rλ, we give the conditions to be a circular helix. Furthermore, we discuss ruled surfaces of type A generated via the curve rλand the vector D which is defined as tangent of the curve rλin 3-dimensional Galilean space. The constructed ruled surfaces also appear in two ways. The first is constructed with the curve rλ(s) = r(s)+λT(s) and the non-isotropic vector D. The second is formedby the curve rλ= r(s) + λ2N + λ3B and the non-isotropic vector D. We calculate the distribution parameters of the constructed ruled surfaces and we show that the ruled surfaces are developable. Finally, we provide examples and visuals to back up our research.

Panakhov, Etibar S.; Sat, Murat

In this paper an inverse problem by two given spectrum for a secondorder differential operator with coulomb singularity of the type Ax in zero point ( here A is constant), is studied. It is well known that two spectrum λn and μn uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0;p] : The aim of this paper is to prove the generalized degeneracy of the kernel K(x; t) . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference eq(x)q∼(x).