Music genre classification has a significant role in information retrieval for the organization of growing collections of music. It is challenging to classify music with reliable accuracy. Many methods have utilized handcrafted features to identify unique patterns but are still unable to determine the original music characteristics. Comparatively, music classification using deep learning models has been shown to be dynamic and effective. Among the many neural networks, the combination of a convolutional neural network (CNN) and variants of a recurrent neural network (RNN) has not been significantly considered. Additionally, addressing the flaws in the particular neural network classification model, this paper proposes a hybrid architecture of CNN and variants of RNN such as long short-term memory (LSTM), Bi-LSTM, gated recurrent unit (GRU), and Bi-GRU. We also compared the performance based on Mel-spectrogram and Mel-frequency cepstral coefficient (MFCC) features. Empirically, the proposed hybrid architecture of CNN and Bi-GRU using Mel-spectrogram achieved the best accuracy at 89.30%, whereas the hybridization of CNN and LSTM using MFCC achieved the best accuracy at 76.40%.

An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters $\lambda$, $\alpha$ and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.

This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters $\alpha$ and $\lambda$ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A-statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters $\alpha$ and $\lambda ,$ and they propose better approximation results.

Integral equations, which are defined as “the equation containing an unknown function under the integral sign”, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer theory. A special case of these equations, known as the quadratic Chandrasekhar integral equation, given by $x\left(s\right)=1+\lambda x\left(s\right){\int }_0^1\frac{s}{t+s}x\left(t\right)dt,$ can be very often encountered in many applications, where x is the function to be determined, $\lambda$ is a parameter, and $t,s\in [0,1]$. In this paper, using a fixed-point theorem, the existence conditions for the solution of Fredholm integral equations of the form $\chi \left(l\right)=\varrho \left(l\right)+\chi \left(l\right){\int }_p^{q}k(l,z)\left(V\chi \right)\left(z\right)dz$ are investigated in the space $C_{\omega }\left[p,q\right],$ where $\chi$ is the unknown function to be determined, V is a given operator, and $\varrho ,k$ are two given functions. Moreover, certain important applications demonstrating the applicability of the existence theorem presented in this paper are provided.

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, $x\left(t\right)=p\left(t\right)+x\left(t\right){\int }_0^{1}k(t,\tau )\left(Tx\right)\left(\tau \right)d\tau ,$ where $p,k$ are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted.