In this article, we extract stochastic solutions for the perturbed chiral nonlinear Schrödinger equation (PCNLSE) forced by multiplicative noise in Itô sense with the aid of exp $[-\phi (\xi )]$-expansion and unified solver methods. The PCNLSE meditate on the quantum behaviour, like quantum features are closely related to its particular features. The proposed techniques introduce the closed form structure of waves in explicit form. The behaviour of the gained solutions are of qualitatively different nature, based on the physical parameters. The acquired solutions are extremely viable in nonlinear optics, superfluid, plasma physics, electromagnetism, nuclear physics, industrial studies and in many other applied sciences. We also illustrate the profile pictures of some acquired solutions to show the physical dynamical representation of them, utilizing Matlab release. The proposed techniques in this article can be implemented to other complex equations arising in applied sciences.

Expanding on our research, this paper introduced novel generalizations of H ölder's and Minkowski's dynamic inequalities on diamond alpha time scales. Specifically, as particular instances of our findings, we replicated the discrete inequalities established when $\mathbb{T}\mathbb{=}\mathbb{N}$. Furthermore, our investigation extended to the continuous case with $\mathbb{T}\mathbb{=}\mathbb{R}$, revealing additional inequalities that are both new and valuable for readers seeking a comprehensive understanding of the topic.

This paper contains some new reverse dynamic inequalities of Hilbert-type on delta time scale calculus using mean inequality by applying reverse Hölder's inequality, chain rule on time scales, integration by parts, and the mean inequality. As special cases of our results, we get the discrete, continuous, and quantum analogs of inequalities, i.e., when $\mathbb{T}\mathbb{=}\mathbb{N}$, $\mathbb{T}\mathbb{=}\mathbb{R}$ and $\mathbb{T}\mathbb{=}{q}^{\mathbb{N}}$ for $q>1$.

Early diagnosis of heart disease is vital for reducing mortality and improving patient outcomes; yet, accurate prediction remains a significant challenge owing to the complexity and high dimensionality of medical data. Data preprocessing is essential for overcoming these issues by cleaning, transforming, reducing, and balancing data to provide reliable inputs for feature selection and classification. This study introduces an improved chi-square ( ${\chi }^2$) feature selection framework combined with multiple classifiers to enhance predictive performance. Our method was applied to Cleveland heart disease and diabetes datasets, where numeric attributes were discretized into categorical values, enabling ${\chi }^2$ to select the most informative features while eliminating redundancy. Several classifiers, including support vector machine (SVM), logistic regression (LR), K-nearest neighbors (KNN), and naive Bayes (NB), were trained using both the reduced subset and the complete feature set. Results show that the preprocessing include ${\chi }^2$ feature selection, achieved the highest performance. On the Cleveland dataset, the model attained a mean accuracy of 93.72%, precision of 94.01%, recall of 93.72%, F1-score of 93.74%, and an area under the curve(AUC) of 97.87%, while on the diabetes dataset, it achieved mean values of 93.55% accuracy, 94.23% precision, 93.55% recall, 93.48% F1-score, and an AUC 93.53%. The main contribution of this work lies in integrating discretization with ${\chi }^2$ based selection to produce a compact and discriminative feature subset. With a minimal number of selected features, the proposed approach delivers robust, accurate, and computationally efficient heart disease prediction, outperforming existing methods.