Initial Value Problems in the Time-Frequency Domain

2013 ◽  
pp. 189-197
Author(s):  
Lorenzo Galleani
Keyword(s):  
Frequency Domain ◽  
Initial Value Problems ◽  
Initial Value ◽  
Time Frequency

scholarly journals Measurement of Film Structure Using Time-Frequency-Domain Fitting and White-Light Scanning Interferometry

Machines ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 336
Author(s):  
Xinyuan Guo ◽  
Tong Guo ◽  
Lin Yuan
Keyword(s):  
Frequency Domain ◽  
White Light ◽  
Cross Correlation ◽  
Three Dimensional ◽  
Film Structure ◽  
Initial Value ◽  
Time Frequency ◽  
Fitting Method ◽  
Time Domains ◽  
A New Technique

A new technique is proposed for measuring film structure based on the combination of time- and frequency-domain fitting and white-light scanning interferometry. The approach requires only single scanning and employs a fitting method to obtain the film thickness and the upper surface height in the frequency and time domains, respectively. The cross-correlation function is applied to obtain the initial value of the upper surface height, thereby making the fitting process more accurate. Standard films (SiO2) with different thicknesses were measured to verify the accuracy and reliability of the proposed method, and the three-dimensional topographies of the upper and lower surfaces of the films were reconstructed.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

scholarly journals Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2023
Author(s):  
Christopher Nicholas Angstmann ◽  
Byron Alexander Jacobs ◽  
Bruce Ian Henry ◽  
Zhuang Xu
Keyword(s):  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Integral Transform ◽  
Initial Value ◽  
Intrinsic Nature ◽  
Recent Interest ◽  
Special Cases ◽  
Singular Kernels

There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities.

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