The linear canonical Hankel type transformations associated with translation and convolution

This paper is the study of Hankel type translation and Hankel type convolution for linear canonical Hankel type transformations. In this paper, I have studied some inequalities associated with Hankel type translation and Hankel type convolution. Also, I have studied some applications of linear canonical Hankel transformation to a canonical convolution integral equation and a generalized nonlinear parabolic equation.

Pseudo-differential operator in the framework of linear canonical transform domain

The main goal of this paper is to study properties of the linear canonical transform (LCT) on Schwartz-type space [Formula: see text]. The symbol class [Formula: see text] is introduced. The pseudo-differential operator (p.d.o.) involving LCT is defined and also some of its properties including boundedness are investigated in Sobolev-type space. Kernel and integral representation of p.d.o. are obtained. Some applications of LCT to generalized partial differential equations and canonical convolution integral equation have been solved.

Estimation of Blood Glucose Concentration During Endurance Sports

In this paper, we describe a new statistical approach to estimate blood glucose concentration along time during endurance sports based on measurements of glucose concentration in subcutaneous interstitial tissue. The final goal is the monitoring of glucose concentration in blood to maximize performance in endurance sports. Blood glucose concentration control during and after aerobic physical activity could also be useful to reduce the risk of hypoglycemia in type 1 diabetes mellitus subjects. By means of a low invasive technology known as "continuous glucose monitoring", glucose concentration in subcutaneous interstitial tissue can now be measured every five minutes. However, it can be expressed as function of blood glucose concentration along time by means of a convolution integral equation. In the training phase of the proposed approach, based on measurements of glucose concentration in both artery and subcutaneous interstitial tissue during physical activity, the parameters of the convolution kernel are estimated. Then, given a new subject performing aerobic physical activity, a deconvolution problem is solved to estimate glucose concentration in blood from continuous glucose monitoring measurements

A General Visco-Hyperelastic Model for Dielectric Elastomers and Its Efficient Simulation Based on Complex Frequency Representation

A general visco-hyperelastic model for dielectric elastomers (DE) is presented in this paper, derived from the Quasi-Linear Viscoelastic (QLV) framework. To gain a physical insight into the time-dependent constitutive relation and solve it efficiently, a complex frequency representation of the convolution integral equation, with the legible form of block-scheme, is specifically constructed, in which the viscoelastic stress is interpreted considering the instantaneous response (depicted by Yeoh strain energy potential) as a signal filtered by a linear system (superposition of characteristic modes of the time relaxation function, i.e., Prony series). By incorporating the effects of electrostatic pressure, the model is further extended to the electromechanical coupling state, which can be expediently implemented by the general software, MATLAB/Simulink. Comparisons of the theoretical predictions from the proposed model with the experimental results previously reported (for VHB elastomers) show good agreements over a wide range of stretch rates (from 10-4 to ~ 1 s-1), whether the membrane is only subjected to large mechanical deformations, or undergoes electric loads simultaneously.

The product of generalized polynomials sets pertaining to a class of convolution integral equations

The purpose of this paper is to obtain a certain class of convolution integral equation of Fredholm type with the product of two generalized polynomials sets. Using of the Mellin transform technique; we have established solution of the integral equation.