Gelfand, Retakh, Serconek and Wilson, in [3], defined a graded algebra AΓ attached to any finite ranked poset Γ a generalization of the universal algebra of pseudo-roots of noncommutative polynomials. This algebra has since come to be known as the splitting algebra of Γ. The splitting algebra has a secondary filtration related to the rank function on the poset and the associated graded algebra ...

In this paper swarm intelligence based PID controller tuning is proposed for a nonlinear ball and hoop system. Particle swarm optimization (PSO), Artificial bee colony (ABC), Bacterial foraging optimization (BFO) is some example of swarm intelligence techniques which are focused for PID controller tuning. These algorithms are also tested on perturbed ball and hoop model. Integral square error (...

In this paper, we define the notion of minimal prime ideals hoops and investigate some properties them. Then by using annihilators, study relation between annihilators. Also, introduce zero divisors elements prove that set all is a union hoop. Finally, notions maximal hoop, two new as p-ideal m-ideal. them every semi-simple hoop an m-ideal it.

An interesting generalization of hoop-algebras and commutative residuated lattices is the concept quasi-ordered systems (shortly QRS) introduced in 2018 by Bonzio Chajda. Quasi-ordered system an integral monoid with two internal binary operations interconnected a residuation connection. This specificity reason for complexity this algebraic structure existence significant number substructures it...

In this paper, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the paraGrassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed. The pseud...

Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control techniques. In contrast to the standard use, we describe the dynamics of the system at full length; in addition to the mode where the ball rolls on the (outer) ho...