scholarly journals On the Solutions of Three-Variable Frobenius-Related Problems Using Order Reduction Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tian-Xiao He ◽  
Peter J.-S. Shiue ◽  
Rama Venkat
Keyword(s):  
Open Problem ◽  
Related Problem ◽  
Order Reduction ◽  
System Of Equations ◽  
Number Of Solutions ◽  
New Approach ◽  
Nonnegative Solutions ◽  
Interesting Open Problem ◽  
Reduction Methods ◽  
Reduction Approach

This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture.

scholarly journals The bilinear method: A new stability-preserving order reduction approach

2002 ◽  
Vol 216 (5) ◽  
pp. 429-436
Author(s):  
T N Lucas
Keyword(s):  
Linear System ◽  
System Parameter ◽  
Transfer Functions ◽  
Order Reduction ◽  
Bilinear Method ◽  
Bilinear Transformation ◽  
New Approach ◽  
Reduction Approach

A new way of reducing the order of linear system transfer functions is presented. It guarantees stability in the approximation of stable systems and differs from existing stability-preserving methods by taking into account whole system parameter information when obtaining the approximate poles, not just that of the system poles. It uses a bilinear transformation in the process, which renders the method more flexible than traditional techniques. Examples are given to highlight the advantages of the new approach.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

scholarly journals A model order reduction approach to create patient-specific mechanical models of human liver in computational medicine applications

2019 ◽  
Vol 170 ◽  
pp. 95-106 ◽  
Author(s):  
Nathan Lauzeral ◽  
Domenico Borzacchiello ◽  
Michael Kugler ◽  
Daniel George ◽  
Yves Rémond ◽  
...  
Keyword(s):  
Human Liver ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Patient Specific ◽  
Model Order ◽  
Mechanical Models ◽  
Reduction Approach

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

scholarly journals Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models

2018 ◽  
Vol 51 (3) ◽  
pp. 465-483 ◽  
Author(s):  
Peter Benner ◽  
Roland Herzog ◽  
Norman Lang ◽  
Ilka Riedel ◽  
Jens Saak
Keyword(s):  
Model Order Reduction ◽  
Sensor Placement ◽  
Order Reduction ◽  
Optimal Sensor Placement ◽  
Model Order ◽  
Reduction Methods
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