In this paper we study the Gross heat equation perturbed by noises with the initial condition being a generalized function. The noises are given by either a white noise or a space-time white noise. The main technique we use is the representation of the Gross Laplacian as a convolution operator. It enables us to apply the convolution calculus on a suitable distribution space to obtain the explic...

This paper presents a path planning method considering physical limits for two-wheeled mobile robots (TMRs). A convolution operator is used to generate the center velocity trajectory to travel the distance along predefined Bezier curve while considering the physical limits. The trajectory gained through convolution does not consider the rotating angle of TMR, so we present a transformational me...

We propose the Wavelet-based Inverse Halftoning via Deconvolution (WInHD) algorithm to perform inverse halftoning of error-diffused halftones. WInHD is motivated by our realization that inverse halftoning can be formulated as a deconvolution problem under Kite et al.’s linear approximation model for error diffusion halftoning. Under the linear model, the error-diffused halftone comprises the or...

Convolutional neural networks have become a main tool for solving many machine vision and machine learning problems. A major element of these networks is the convolution operator which essentially computes the inner product between a weight vector and the vectorized image patches extracted by sliding a window in the image planes of the previous layer. In this paper, we propose two classes of su...

Making use of the convolution operator we introduce a new class of analytic functions in the open unit disk and investigate some subordination results. c ©2017 All rights reserved.

Waveform relaxation methods are iterative methods for the solution of systems of ordinary differential equations. The convergence analysis of waveform relaxation methods traditionally uses the theory of Volterra convolution equations. More specifically, the convergence theory is typically based on a theorem of Paley and Wiener that gives a condition for the solution of a linear Volterra convolu...

We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...