Synchronous homopolar machines (SHM) with excitation winding on the stator have attracted the attention of researchers for many decades due to their high reliability. They are used in a variety of applications such as aircraft and railway generators and traction motors. At the same time, the three-dimensional structure of their magnetic circuit makes the problem of their analysis and optimization challenging. This problem becomes even more complicated when considering an SHM with hybrid excitation, with ferrite magnets in the rotor slots. The article proposes a mathematical procedure for optimizing a synchronous homopolar generator with hybrid excitation based on the single-criterion Nelder-Mead method and two-dimensional finite element analysis (FEA). The use of the Nelder-Mead method compared to multicriteria methods and 2D FEA compared to 3D FEA makes possible to significantly reduce the computational burden. As a result of optimization, the power loss and torque ripples of the generator are significantly reduced. The article also compares the characteristics of synchronous homopolar generators with and without ferrite magnets.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

The performance in terms of minimal Bayes’ error probability for detection of a high-dimensional random tensor is a fundamental under-studied difficult problem. In this work, we consider two Signal to Noise Ratio (SNR)-based detection problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size Nq  R, i.e, for 1  q  Q, where R, Nq ! ¥ with R1/q/Nq converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear (M1, . . . ,MQ)-rank with large factors of size Nq  Mq, i.e, for 1  q  Q, where Nq,Mq ! ¥ with Mq/Nq converge towards a finite constant. The detection of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the error probability is mathematically intractable. To circumvent this technical difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s?. In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s? = 1/2) can not solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s?. However, thanks to powerful random matrix theory tools, a simple analytical expression of s? is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. A main conclusion of this work is that the BUB is the tightest bound at low SNRs. This property is, however, no longer true for higher SNRs.

The various methods used to choose the profile shift coefficients, primarily the so-called equalizations, were based on assumed advantages without physical evidence proving them. In this paper a new calculation method is presented for determining profile shift coefficient. The procedure gives the pair of values ​​of the profile shift coefficients, in which case, under the given load, the resulting bending stress will be of the lowest possible value.

The automotive industry has witnessed a significant push towards increased fuel efficiency and reduced carbon emissions. Among many factors influencing overall vehicle efficiency, aerodynamic drag is a critical consideration, accounting for a substantial portion of fuel consumption. Our investigation focused on the drag coefficients of three prominent 2023 passenger car models – the Toyota Corolla, Hyundai Elantra, and Kia Soul. Using ANSYS Fluent to perform computational fluid dynamics, we demonstrated an inverse correlation between drag force and gas mileage, underlining the significance of aerodynamic design in fuel efficiency. Notably, the Hyundai Elantra emerged as the most aerodynamically efficient of the three vehicles, followed closely by the Toyota Corolla. In contrast, the boxier-designed Kia Soul exhibited significantly higher drag coefficients and drag forces, rendering it the least efficient of the trio. These findings emphasize the importance of environmental factors in car design. Shaping aerodynamic profiles directly impacts fuel efficiency, stability, and overall performance.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.