The convolution of two φ-convex functions is estimated by means of an inequality of Hadamard type. The sharpness of this inequality is discussed. As consequence, few inequalities for the convolution ...

The convolution of two rational Laplace transform denominators can be calculated using their resultant, while that of the two rational Z-transform transfer functions can be found using Newton’s ...

In this paper we study a class of functional operators under which the convexity of convex set functions is preserved. In particular, convolution of convex set functions is defined and its convexity ...

Convolutional neural network is the most important algorithm in the field of deep learning. The traditional convolution neural network usually uses Sigmoid or Relu as the activation function, but the ...

In this study, we aim to interpret the hidden semantics of each unit within convolutional neural networks by abstracting local activated patterns of each neuron into corresponding global functions.