Development of control technology using an algebraic model of ultrasound — technology to control nonlinear phenomena according to specific objectives.

The Ultrasonic System Research Institute has developed a technology to control phenomena related to the nonlinearity of ultrasound, using a model based on the category of Monoids in absolute mathematics.
The entire phenomenon of basic ultrasonic irradiation is treated as a Ring, while the phenomena caused by cavitation are modeled as an Abelian group, and those caused by acceleration are modeled as a Monoid (a unital algebra with a multiplicative identity).
In mathematics, the complexity of rings is examined by distinguishing the relationships between Abelian groups and Monoids, and this has been correspondingly applied to ultrasonic phenomena as follows:
Abelian group: Operations related to addition correspond to cavitation phenomena.
Monoid: Operations related to multiplication correspond to acceleration phenomena.
The measurement and analysis results obtained so far using ultrasonic testers have been adapted to the Monoid model, leading to numerous applications that can be expanded into real-world phenomena (note), and it has been developed as a full-fledged logical model.
Note: Particularly the interactions of nonlinear phenomena.
We believe that it can further evolve into a more practical logical model in the future.


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