iosr-Jm   Volume-22 ~ Issue-1 ~ Jan. – Feb. 2026

Abstract : In this study, data of 113,549 songs is used to examine the factors that can influence the popularity of the track in the presence of Spotify. The study question was whether the intrinsic sound characteristic of a work is less likely to predict the extrinsic metadata such as genre. The correlation diagnostic and research statistics obtained after the preprocessing phase of the research demonstrated a weak correlation of popularity with auditory features and instrumentalness showed the strongest negative correlation (r = -0.127). Higher popularity ranges were confirmed....

Keywords: Spotify, Track Popularity, Audio Features, Metadata, Genre Classification, Predictive Modeling

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Abstract : Whether a polynomial with rational coefficients is irreducible over the field rational numbers, Q \mathbb{Q}, is one of the important problems posed in algebra which has a wide application in number theory, field theory, and computational aspects of mathematics. Eisenstein’s Criterion is a classical result in number theory. It is a nice and powerful result for irreducibility of integers. Many polynomials do not respect the strict assumptions required by these classical criteria. Therefore, they are not directly applicable. To address this limitation, various families of extended versions of Eisenstein’s Criterion have been derived. Essentially, appropriate transformations of polynomials, such as translations, scalings, compositions, etc., will ruin the polynomial but probably leave its irreducible properties intact....

Keywords: Polynomial Irreducibility, Irreducibility Criteria, Rational Field Q, Gauss’s Lemma, Eisenstein’s Criterion.

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