scholarly journals Iterations and Groups of Formal Transformations

2021 ◽  
Vol 14 (5) ◽  
pp. 584-588
Author(s):  
Oleg V. Kaptsov ◽  
Keyword(s):  
Existence Theorem ◽  
Interpolation Problem ◽  
Transformation Groups ◽  
Square Root ◽  
Area Preserving

In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser’s existence theorem for an interpolation problem. We give examples of formal transformation groups such that the iteration problem has a solution for every element of the groups

About the Complexity of Square Root Extraction Algorithms in Finite Fields and Residue Rings

Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Square Root ◽  
Root Extraction

The digital function filters – algorithms and applications

2013 ◽  
Vol 61 (2) ◽  
pp. 371-377
Author(s):  
M. Siwczyński ◽  
A. Drwal ◽  
S. Żaba
Keyword(s):  
Digital Filters ◽  
Phase Shifters ◽  
Square Root ◽  
Real Power ◽  
The Real ◽  
Distributed Parameters ◽  
Digital Modeling ◽  
Analysis And Synthesis ◽  
Basic Functions ◽  
Recursive Formulas

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

Log-Conformation and Square Root-Conformation Transformations in High Weissenberg Number Flows

2019 ◽  
Author(s):  
Beatriz Liara Carreira ◽  
Analice Costacurta Brandi ◽  
Laison Junio da Silva Furlan ◽  
Matheus Tozo de Araujo ◽  
Leandro Franco de Souza
Keyword(s):  
Weissenberg Number ◽  
Square Root
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