scholarly journals Linear fractional transformations in rings and modules

1984 ◽  
Vol 56 ◽  
pp. 251-290 ◽  
Author(s):  
N.J. Young
Keyword(s):  
Linear Fractional Transformations

Note on Best Approximation of |x|

1979 ◽  
Vol 22 (3) ◽  
pp. 363-366
Author(s):  
Colin Bennett ◽  
Karl Rudnick ◽  
Jeffrey D. Vaaler
Keyword(s):  
General Problem ◽  
Uniform Approximation ◽  
Best Approximation ◽  
Best Uniform Approximation ◽  
Linear Fractional Transformations ◽  
Symmetric Complex ◽  
Image Position ◽  
Complex Valued ◽  
Special Case

In this note the best uniform approximation on [—1,1] to the function |x| by symmetric complex valued linear fractional transformations is determined. This is a special case of the more general problem studied in [1]. Namely, for any even, real valued function f(x) on [-1,1] satsifying 0 = f ( 0 ) ≤ f (x) ≤ f (1) = 1, determine the degree of symmetric approximationand the extremal transformations U whenever they exist.

scholarly journals Groups generated by elements with rational fixed points

1997 ◽  
Vol 40 (1) ◽  
pp. 19-30 ◽  
Author(s):  
A. W. Mason
Keyword(s):  
Normal Subgroup ◽  
Fixed Points ◽  
Large Class ◽  
Integral Domain ◽  
Structure Theorem ◽  
Quotient Field ◽  
Linear Fractional Transformations ◽  
Krull Domain ◽  
Dedekind Domains ◽  
Precise Version

Let R be a commutative integral domain and let S be its quotient field. The group GL2(R) acts on Ŝ = S ∪ {∞} as a group of linear fractional transformations in the usual way. Let F2(R, z) be the stabilizer of z ∈ Ŝ in GL2(R) and let F2(R) be the subgroup generated by all F2(R, z). Among the subgroups contained in F2(R) are U2(R), the subgroup generated by all unipotent matrices, and NE2(R), the normal subgroup generated by all elementary matrices.We prove a structure theorem for F2(R, z), when R is a Krull domain. A more precise version holds when R is a Dedekind domain. For a large class of arithmetic Dedekind domains it is known that the groups NE2(R),U2(R) and SL2(R) coincide. An example is given for which all these subgroups are distinct.

Performance of the Bond Graph Approach for the Detection and Localization of Faults of a Refrigerator Compartment Containing an Ice Quantity

2018 ◽  
Vol 26 (03) ◽  
pp. 1850028 ◽  
Author(s):  
Abderrahmene Sellami ◽  
Emna Aridhi ◽  
Dhia Mzoughi ◽  
Abdelkader Mami
Keyword(s):  
Bond Graph ◽  
Heat Fluxes ◽  
Point Of View ◽  
Internal Cooling ◽  
Linear Fractional Transformations ◽  
Insulation Failure ◽  
Water Container ◽  
Simulation Results ◽  
Heat Transfers ◽  
Detection And Localization

In this paper, a robust fault diagnosis for a refrigerator compartment containing a quantity of ice using the bond graph (BG) approach is performed by linear fractional transformations (LFTs). The BG model describes heat transfers supported by the amount of ice placed in the refrigerator compartment, as well as a water container. The LFT modeling of BG elements offers advantages from the point of view of structural analysis and data processing implementation. We have introduced four faults, which consist of ice temperature rise, water leakage, insulation failure at the hot walls of the refrigerator and an increase of the internal temperature due to poor door sealing. The faults are in the form of additional heat fluxes. The simulation results show the effectiveness of the proposed method for detecting and localizing faults. In addition, the lack of door sealing has the most influence on the temperatures in the internal cooling space, water, and ice compared to the other faults.

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