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Yayın Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions(Elsevier Science Inc, 2018-02-15) Sakar, Fethiye Müge; Aydoğan, Seher MelikeLet's take f(z) = h (z) + <(g(z))over bar> which is an univalent sense-preserving harmonic functions in open unit disc D = {z : vertical bar z vertical bar < 1}. If f (z) fulfills vertical bar w(z)vertical bar = |g'(z)/h'(z)vertical bar < m, where 0 <= m < 1, then f(z) is known m-quasiconformal harmonic function in the unit disc (Kalaj, 2010) [8]. This class is represented by S-H(m).The goal of this study is to introduce certain features of the solution for non- linear partial differential equation <(f)over bar>((z) over bar) = w(z)f(z) when vertical bar w(z)vertical bar < m, w(z) (sic) m(2)(b(1)-z)/m(2)-b(1)z, h(z) is an element of S*(A, B). In such case S*(A, B) is known to be the class for Janowski starlike functions. We will investigate growth theorems, distortion theorems, jacobian bounds and coefficient ineqaulities, convex combination and convolution properties for this subclass.Yayın Adaptive convolution kernel for artificial neural networks(Academic Press Inc., 2021-02) Tek, Faik Boray; Çam, İlker; Karlı, DenizMany deep neural networks are built by using stacked convolutional layers of fixed and single size (often 3 × 3) kernels. This paper describes a method for learning the size of convolutional kernels to provide varying size kernels in a single layer. The method utilizes a differentiable, and therefore backpropagation-trainable Gaussian envelope which can grow or shrink in a base grid. Our experiments compared the proposed adaptive layers to ordinary convolution layers in a simple two-layer network, a deeper residual network, and a U-Net architecture. The results in the popular image classification datasets such as MNIST, MNIST-CLUTTERED, CIFAR-10, Fashion, and ‘‘Faces in the Wild’’ showed that the adaptive kernels can provide statistically significant improvements on ordinary convolution kernels. A segmentation experiment in the Oxford-Pets dataset demonstrated that replacing ordinary convolution layers in a U-shaped network with 7 × 7 adaptive layers can improve its learning performance and ability to generalize.
