In modern industrial manufacturing processes, induction motors are broadly utilized as industrial drives. Online condition monitoring and diagnosis of faults that occur inside and/or outside of the Induction Motor Drive (IMD) system make the motor highly reliable, helping to avoid unscheduled downtimes, which cause more revenue loss and disruption of production. This can be achieved only when the irregularities produced because of the faults are sensed at the moment they occur and diagnosed quickly so that suitable actions to protect the equipment can be taken. This requires intelligent control with a high-performance scheme. Hence, a Field Programmable Gate Array (FPGA) based on neuro-genetic implementation with a Back Propagation Neural network (BPN) is suggested in this article to diagnose the fault more efficiently and almost instantly. It is reported that the classification of the neural network will provide the output within 2 µs although the clone procedure with microcontroller requires 7 ms. This intelligent control with a high-performance technique is applied to the IMD fed by a Voltage Source Inverter (VSI) to diagnose the fault. The proposed approach was simulated and experimentally validated.

Different types of number theories such as elementary number theory, algebraic number theory and computational number theory; algebra; cryptology; security and also other scientific fields like artificial intelligence use applications of quadratic fields. Quadratic fields can be separated into two parts such as imaginary quadratic fields and real quadratic fields. To work or determine the structure of real quadratic fields is more difficult than the imaginary one. The Dirichlet class number formula is defined as a special case of a more general class number formula satisfying any types of number field. It includes regulator, ℒ -function, Dedekind zeta function and discriminant for the field. The Dirichlet’s class number h ( d ) formula in real quadratic fields claims that we have h ( d ) . log ε d = Δ . ℒ ( 1 , χ d ) h\left(d \right).log {\varepsilon _d} = \sqrt {\Delta} {\scr L} \left({1,\;{\chi _d}}\right) for positive d > 0 and the fundamental unit ɛ _d of ℚ ( d ) {\rm{\mathbb Q}}\left({\sqrt d} \right) . It is seen that discriminant, ℒ -function and fundamental unit ɛ _d are significant and necessary tools for determining the structure of real quadratic fields. The focus of this paper is to determine structure of some special real quadratic fields for d > 0 and d ≡ 2,3 ( mod 4). In this paper, we provide a handy technique so as to calculate particular continued fraction expansion of integral basis element w _d , fundamental unit ɛ _d , and so on for such real quadratic number fields. In this paper, we get fascinating results in the development of real quadratic fields.

In this present paper, we establish the existence and uniqueness of the common fixed point theorem for self-maps in C*-algebra valued b-metric spaces. Besides, we give example to illustrate our theorem. Findings obtained in this paper unify, generalize, and complement the comparable results from the current literature.

The aim of this paper is to obtain the real quadratic fields Q (root d) including omega(d) = [a(0) ; ; /gamma, gamma, ..., gamma, a(l) } l-1 where l = l (d) is the period length and gamma is a positive odd integer. Moreover, we have considered a new perspective to determine the fundamental units epsilon(d) and got important results on Yokoi's invariants n(d) and m(d) [since they satisfy necessary and sufficient conditions related to Ankeny-Artin-Chowla conjecture (A.A.C.C), give bounds for fundamental units and so on...] for such types of fields.