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A Meshless Approach to Study Rarefied Gas Flows in Lid-Driven Square Cavities

2026-04-28T12:12:49Z

Title: A Meshless Approach to Study Rarefied Gas Flows in Lid-Driven Square Cavities Authors: Himanshi; Gupta, Vinay Kumar Abstract: This paper investigates rarefied gas flows in a lid-driven square cavity using the method of fundamental solutions (MFS). Unlike traditional techniques requiring extensive computational resources and meshing for simulating rarefied gas flows in complex geometries, the MFS bypasses the need for mesh generation and offers a promising alternative. This research focuses on rarefied gas flows confined within an isothermal square cavity with single-sided and two-sided lid-driven configurations. The coupled constitutive relations (CCR) have been adopted in the present work to capture rarefaction effects. © The Author(s) 2026.

A class of simple derivations of polynomial ring k[x 1,x 2,…,x n]

2026-04-28T12:12:49Z

Title: A class of simple derivations of polynomial ring k[x 1,x 2,…,x n] Authors: Mishra, Sumit Chandra; Mondal, Dibyendu; Shukla, Pankaj Abstract: Let k be a field of characteristic zero. Let m and (Formula presented.) be positive integers. For (Formula presented.), let (Formula presented.) with the k-derivation (Formula presented.) given by (Formula presented.). We prove that for integers (Formula presented.) and (Formula presented.), (Formula presented.) is a simple k-derivation of (Formula presented.) and (Formula presented.) contains no units. This generalizes a result of D. A. Jordan [5]. We also show that the isotropy group of (Formula presented.) is conjugate to a subgroup of translations. © 2025 Taylor & Francis Group, LLC.

CI-RKM: A Class-Informed Approach to Robust Restricted Kernel Machines

2026-04-28T12:12:30Z

Title: CI-RKM: A Class-Informed Approach to Robust Restricted Kernel Machines Authors: Mishra, Ritik; Akhtar, Mushir; Tanveer, M. Abstract: Restricted kernel machines (RKMs) represent a versatile and powerful framework within the kernel machine family, leveraging conjugate feature duality to address a wide range of machine learning tasks, including classification, regression, and feature learning. However, their performance can degrade significantly in the presence of noise and outliers, which compromises robustness and predictive accuracy. In this paper, we propose a novel enhancement to the RKM framework by integrating a class-informed weighted function. This weighting mechanism dynamically adjusts the contribution of individual training points based on their proximity to class centers and class-specific characteristics, thereby mitigating the adverse effects of noisy and outlier data. By incorporating weighted conjugate feature duality and leveraging the Schur complement theorem, we introduce the class-informed restricted kernel machine (CI-RKM), a robust extension of the RKM designed to improve generalization and resilience to data imperfections. Experimental evaluations on benchmark datasets demonstrate that the proposed CI-RKM consistently outperforms existing baselines, achieving superior classification accuracy and enhanced robustness against noise and outliers. Our proposed method establishes a significant advancement in the development of kernel-based learning models, addressing a core challenge in the field. Codes are available at https://github.com/mtanveer1/CI-RKM. © 2025 IEEE.

Comparison and distortion properties of new distance ratio metrics

2026-04-28T12:12:49Z

Title: Comparison and distortion properties of new distance ratio metrics Authors: Maji, Bibekananda; Naskar, Pritam; Sahoo, Swadesh Kumar Abstract: In 1979, Gehring and Osgood introduced the distance ratio metric, and later Vuorinen proposed another version of this metric. This manuscript investigates a new variant of these metrics defined on bounded domains in Rn, n≥2. We show that the metric mD, recently introduced by the authors, is the inner metric of one of the newly defined metrics corresponding to Vuorinen's version of the distance ratio metric. We also explore its relationships with several well-known hyperbolic-type metrics. The paper presents ball inclusion properties of the metrics associated with mD and other hyperbolic-type metrics. Their distortion properties are also examined under several important classes of mappings. Furthermore, as an application, we demonstrate that these metrics can be used to characterize uniform domains. © 2026 Elsevier Inc.