The paper introduces a new method to determine all rank two Nichols algebras of diagonal type over fields of positive characteristic.

Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum g...

Time delays are components that make time-lag in systems response. They arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. In this work, we implement Genetic Algorithm (GA) in determining PID controller parameters to compensate the delay in First Order Lag plus Time Delay (FOLPD) and compare the results with Iterative Method a...

Proportional-integral-derivative (PID) controllers are widely used in industrial control systems because of the reduced number of parameters to be tuned. The most popular design technique is the Ziegler–Nichols method, which relies solely on parameters obtained from the plant step response. However, besides being suitable only for systems with monotonic step response, the compensated systems wh...

Following is the text of a letter, dated December 23, 1953, from Major General K. D. Nichols, general manager Atomic Energy Commission, to Dr. J. Robert Oppenheimer.

Received July 19, 2017 Revised Oct 20, 2017 Accepted Nov 7, 2017 Line tracking robots have been widely implemented in various applications. Among various control strategies, a proportional-integral-derivative (PID) algorithm has been widely proposed to optimize the performance of a line tracking robot. However, the motivation of using a PID controller, instead of a proportional (P) or a proport...

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

AbstractA Composition control system is discussed in this paper in which the PID controller is tuned using Genetic Algorithm & Ziegler-Nichols Tuning Criteria. Tuning methods for PID controllers are very important for the process industries. Traditional methods such as Ziegler-Nichols method often do not provide adequate tuning. Genetic Algorithm (GA) as an intelligent approach has also been wi...