Nowadays, the automotive industry faces significant challenges in improving energy efficiency and in order to protect the environment. This paper will investigate the potential of energy recovery systems to reduce the substantial waste energy generated by internal combustion engines. Thermal recovery technology including regenerative braking, mechanical flywheels, thermoelectric generators, and electric turbochargers all of these technologies can enhance vehicle energy efficiency. This paper investigates two criteria energy efficiency and feasibility. It has been determined that regenerative braking improves by up to 8% in fuel efficiency. mechanical flywheels improved by 11% in fuel efficiency. respectively. For TEG technology, under a specific environment and using Cúk converters and MPPT control it shows an increase from 14.5% to 22.6%, but lower power output than the previous two technologies. For Electric Turbochargers, it achieves maximum values of 8.4% to 18.4% in enhancement in energy efficiency. The paper also focuses on the feasibility, of regenerative braking the semi-automatic turbocharger is better for driving, mechanical flywheels, compared to traditional hybrid electric vehicles (HEVs), PS-FHV is a workable technology that provides greater fuel economy and quicker acceleration. For thermoelectric generators, it illustrates that it is possible to replace the traditional internal combustion engine with a thermoelectric generator in automotive powertrains and it is suited for future extended-range electric vehicles (EEVs) and hybrid electric vehicles (HEVs). Lastly, regenerative braking provides a novel control strategy is the potential to improve both efficiency and safety. In summary, these technologies have significant potential to improve automotive energy efficiency, and future research could further optimize the application of these technologies to achieve higher energy efficiency and lower environmental impacts. The currently best technology for energy recovery is the regenerative braking and mechanical flywheels. However, thermoelectric generators can have the most potential in the future, especially in extended-range electric vehicles (EEVs) and hybrid electric vehicles (HEVs). Based on the research, hybrid and extended-range electric vehicles have be potential for future markets.

In this paper, we give an introduction to the compact space under Constructive Mathematics, ultimately showing that there exist no computer programs that can always determine if a fundamental group of a constructive compact topological space is trivial or not. We will begin with the non-halting case of the programs, which shows that the fundamental group of our selected set is trivial. From here, we will explore the halting case of the programs, which can be solved by arbitrarily picking a nontrivial subset of our selected set. The main result of this section is that we can show that the algorithm is decidable due to our initial construction, while realizing its contradiction with our input. We want to show that such an algorithm doesn’t exist by employing the proof-by-contradiction method.

The purpose of this study is to understand patterns by observing the acoustic characteristics of naturally produced violin vibrato through direct measurement, comparative analysis with sustained tones, and theoretical modeling. Unlike sustained tones, vibrato introduces periodic oscillations in pitch, amplitude, and harmonic content and combines them to create the timbre of the violin. A detailed analysis of bowed vibrato is conducted to explore potential relationships between vibrato and modulation of pitch, amplitude variation, and timbre shifts. Mathematical models are also used to capture these vibrato effects in the form of equations. In essence, the findings confirm the indispensable role of vibrato in forming the tonal complexity of violin sound, with info useful for improved vibrato synthesis, room acoustic optimization, and violin music education.

This paper aims to derive a recursive relationship of the values of Riemann zeta function at even natural numbers by using the principles of elementary symmetric polynomials, and associations between them and zeta functions, thereby expressing in only terms of previous zeta function’s values. Moreover, this recursive formula is going to be proven equivalently to the explicit formula of

The orbital decay of Kepler-1658b remains a mystery to this day. Many previous authors have searched for this hot Jupiter using ground-based telescopes, with no secure results. Here, I present a search for Kepler-1658b with the data from NASA's Transiting Exoplanet Survey Satellite (TESS). By using the most recent TESS data, I have extended the time baseline of previous observations and was able to perform a more sensitive search. I evaluated the latest data and found further evidence to confirm the shrinking orbit of Kepler-1658b and predict the inspiral time of the system.

This article aims to explore the interaction between sound knowledge and sound perception, especially in subjects with absolute pitch (AP). The study used fMRI scanning technology to explore two specific objectives: first, to test whether the brain system related to sound perception was actually activated when retrieving knowledge related to pitch through language stimuli; The second is to compare the speed and accuracy of subjects with absolute pitch perception and those without absolute pitch perception in terms of sound perception and sound memory retrieval association. The research results are expected to provide support for the view that there is a direct overlap between conceptual knowledge and perceptual systems, and further verify the correctness of the "embodied simulation" theory. In addition, the study also proposed further research directions, namely exploring the influence of absolute pitch ability on spatial perception ability of pitch and the similarities and differences in the neural basis between absolute pitch test subjects and other subjects when corresponding to CMC across modalities.

In this paper, we present two methods to derive the formula for the volume of n-dimensional spheres in Euclidean space and analyze its asymptotic behavior as n approaches infinity using Stirling’s formula. We then establish a connection between the infinite sum of all even-dimensional spheres of radius r and the exponential function through a differential equation. Our findings highlight the decay characteristics of high-dimensional volumes and reveal a novel link between geometry and analysis. This work not only refines classical volume estimation techniques but also offers valuable insights into applications in higher-dimensional mathematics, contributing to fields such as statistical mechanics and theoretical physics.

This study focuses on the history of Catalan numbers, including definitions, formulas, combinatorial meanings, and geometric interpretations. Catalan numbers are a sequence of natural numbers widely used in combinatorial mathematics, often used to represent arrangements of structures such as balanced brackets, binary trees and polygonal triangular dissections. In terms of the definition and properties of symmetry groups, the study includes the structure of orders and subgroups as well as representation theory. Symmetry groups describe the symmetry of geometric objects, including rotations, reflections, and axes of rotational reflections. The connection between Catalan numbers and symmetry groups, including influences and interactions, is further analysed.

This study investigates the connection between the undecidability of certain sets and the problem of determining the position of a point relative to the boundary or exterior of a closed set. We introduce a new algorithm, referred to as Algorithm A, which generates a closed set at regular intervals. By employing a reductio ad absurdum argument, we demonstrate that no algorithm exists that can consistently determine whether a point lies on the boundary or in the exterior of a closed set. This finding highlights the limitations of algorithmic approaches in the context of constructive mathematics.

This paper introduces a simplified approach to finding irreducible polynomials, a fundamental concept in abstract algebra crucial for understanding field and ring structures. Traditionally, identifying these polynomials involves complex computations or heuristic methods. Our study presents a straightforward method by constructing and proving the integrality of the polynomial roots, bridging advanced and elementary mathematical principles. The proposed method utilizes Vieta’s formulas and roots of unity to systematically construct potential roots of an element's irreducible polynomial across various fields. We provide elementary proofs using induction and polynomial properties, demonstrating the method’s effectiveness through examples in both rational and finite fields.