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Volume Info.
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Title
Proceedings of Machine Learning: Integrating machine learning techniques to advance network security - CONFMPCS 2024
Conference Date2024-08-09
WebsiteNotesISBN978-1-83558-493-4 (Print)
978-1-83558-494-1 (Online)
Published Date2024-06-24
EditorsAnil Fernando, University of Strathclyde
Articles
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Open
Access | Article
2024-06-24
Doi: 10.54254/2753-8818/41/20240109
Analyzing musical tones with fourier transformation
This essay delves into the mathematical exploration of musical tones through the application of Fourier Transformation, a pivotal tool in the field of digital signal processing and acoustics. By converting complex musical tones from the time domain to the frequency domain, Fourier Transformation enables the deconstruction of sounds into their constituent frequencies, revealing the unique harmonic structures that contribute to the characteristic timbre of different musical instruments. The focus of this analysis is particularly on the trumpet, chosen for its rich harmonic content and distinctive sound. Through the examination of audio recordings, this study uncovers the fundamental frequency and harmonics of the trumpet, demonstrating how these elements combine to form its unique acoustic fingerprint. The process involves recording, analyzing, and comparing musical tones using software tools like MATLAB and Python, providing an accessible yet profound insight into the intersection of mathematics and music. This essay not only highlights the technical methodology of Fourier Transformation in analyzing musical tones but also explores its practical applications in music theory, digital audio processing, and the broader field of acoustics. The findings underscore the transformative power of mathematical analysis in understanding and appreciating the complex beauty of musical sounds, opening avenues for further research and application in both the scientific and artistic domains.
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Open
Access | Article
2024-06-24
Doi: 10.54254/2753-8818/41/20240105
A method to test the uniform convergence of function series
The series refer to performing infinite addition operations on infinite numbers or functions in a certain order. It is hard to find out whether the positive function series converges uniformly in many cases. In this article, a new method that replacing the sum of function terms series with improper integral will be introduced, which is designed to solve problems that cannot be solved by classical Weierstrass M-test. The Cauchy uniform convergence test will serve as the basis for the entire proof process because it can lead the focus point from the whole sum to the partial sum of the function series, where its value can be easier substituting by the value of the improper integral. After using basic knowledge of the improper integral, the uniform convergence can finally be known. By using this method, testing the uniform convergence of the irregular function series even estimating its value can be possible accomplished.
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Open
Access | Article
2024-06-24
Doi: 10.54254/2753-8818/41/20240107
The application of convex function and GA-convex function
A convex function is a function that maps from a convex subset of a vector space to the set of real numbers. Convex functions have some important properties, such as non-negativity, monotonicity, and convexity, which can help us derive and prove inequalities. This paper explores the concepts of convex functions and GA-convex functions, demonstrating their utility in proving a variety of common and complex inequalities. Beginning with an overview of convex functions and their extension to GA-convex functions, the study shows how these mathematical tools can be effectively utilized in the context of inequality proofs. By leveraging the properties of these functions, the paper successfully establishes rigorous proofs for a range of inequalities, highlighting the versatility and applicability of convex and GA-convex functions in mathematical analysis. The properties convex and GA-convex functions allow us to use it to determine the direction of inequalities, prove inequalities, determine the optimal solution of inequalities, and even prove Cauchy inequalities.