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The hydrophobic property of composite insulators (CIs) is a crucial attribute that prevents the accumulation of significant water content on the surface and ensures smooth operation and prevention of power line surges. However, since the weathering effect gradually reduces the hydrophobicity, periodic monitoring is necessary to ensure the smooth operation of the powerline. Efficient machine learning-based analysis of the CI images collected by the spray method can potentially achieve very high efficacy. However, inconsistency in the shape and size of droplets, the intricate pattern of the droplets, and the lack of color variation of the images, pose a challenge to the prevalent computer vision techniques for categorizing the CIs. This treatise explored a novel, efficient deep-learning paradigm, termed cross-attention vision transformer (CA-ViT) for grading the CI images. The CA-ViT uses both small and large patches to blend spatial features corresponding to a different scale. The network uses a token fusion module to effectively combine the tokens obtained from small and large patches and understand the visual pattern, and characterize droplets of different shapes and sizes by exchanging cross-attentions, which demonstrates its ability to precisely detect small and large droplets, and accurately classify the droplet images. Further, the work also introduces a knowledge distillation (KD) strategy to reduce the computational run time of the model. Exhaustive experimental results have confirmed that our proposed work surpasses state-of-the-art methods.

Change detection (CD) from remote sensing (RS) images using deep learning has been widely investigated in the literature. It is typically regarded as a pixelwise labeling task that aims to classify each pixel as changed or unchanged. Although per-pixel classification networks in encoder-decoder structures have shown dominance, they still suffer from imprecise boundaries and incomplete object delineation at various scenes. For high-resolution RS images, partly or totally changed objects are more worthy of attention rather than a single pixel. Therefore, we revisit the CD task from the mask prediction and classification perspective and propose mask classification-based CD (MaskCD) to detect changed areas by adaptively generating categorized masks from input image pairs. Specifically, it utilizes a cross-level change representation perceiver (CLCRP) to learn multiscale change-aware representations and capture spatiotemporal relations from encoded features by exploiting deformable multihead self-attention (DeformMHSA). Subsequently, a masked cross-attention-based detection transformers (MCA-DETRs) decoder is developed to accurately locate and identify changed objects based on masked cross-attention and self-attention (SA) mechanisms. It reconstructs the desired changed objects by decoding the pixelwise representations into learnable mask proposals and making final predictions from these candidates. Experimental results on five benchmark datasets demonstrate the proposed approach outperforms other state-of-the-art models. Codes and pretrained models are available online at: https://github.com/EricYu97/MaskCD.

In this paper we extend the notions of statistical limit points and statistical cluster points of double sequences of real numbers to I-statistical limit points and I-statistical cluster points of double sequences of real numbers. We study some basic properties of the set of all I-statistical cluster points and the set of all I-statistical limit points of a double sequence of real numbers including their interrelationship. Also introducing additive property of double I-natural density zero sets we present I-statistical analogue of some well known theorems concerning double sequences that are equivalent to the completeness of the real line.

Abstract: Non-linear propagation of dust ion-acoustic (DIA) solitary waves in a multi-component plasma consisting of ions, Cairn’s distributed electrons and immobile dust has been investigated theoretically. Reductive Perturbation Technique (RPT) is used to derive Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. Both compressive as well as rarefactive solitons (compressive in most of the situations) and only compressive mKdV solitons are found to exist for this plasma. Many interesting facts on amplitude as well as width of solitons are established by comparing KdV and mKdV solitons under the same set of different plasma parameters. The investigation is being done in two different modes and found that the non-thermal parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\beta )$$\end{document}and the number of dust charge contained in a immobile dust particle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Z_d)$$\end{document}plays very important role in the formation of both KdV and mKdV solitons.

Higher-order dust–ion acoustic solitary waves are investigated theoretically for a multicomponent relativistic dusty plasma consisting of nonthermal ions, weakly relativistic electrons and mobile dust particles through reductive perturbation technique by deriving modified Korteweg–de Vries (mKdV) equation. Amplitudes of relativistic dust–ion acoustic solitary waves are investigated for different initial streaming speed of ions, weakly relativistic electrons and dust particles and found that there is non-existence region of soliton for some initial streaming of ions as well as electrons. Interestingly, relativistic electron has a region of critical initial streaming speed at which amplitudes of the solitons are equal for different initial streaming of ions whereas for different initial streaming of electrons, the amplitudes of solitons become same after a certain value of initial streaming of ions, which is a salient feature of this investigation. It is also found that the amplitudes of the relativistic dust–ion acoustic solitary waves increase concavely with the increase in dust charges for smaller values of initial streaming of dust particles, whereas the growth of the same is concave for higher initial streaming of dust particles. The width of the relativistic dust–ion acoustic solitary wave is also investigated for different initial streaming of plasma particles.

We prove some basic properties of strong ℐλ{\mathcal{I}_{\lambda}}-statistical convergence of sequences in probabilistic metric spaces and introduce the notion of strong ℐλ{\mathcal{I}_{\lambda}}-statistical cluster point. We also introduce the notion of strong ℐλ{\mathcal{I}_{\lambda}}-statistical Cauchy sequences in probabilistic metric spaces. Further, we establish a connection between strong ℐλ{\mathcal{I}_{\lambda}}-statistical convergence and strong ℐλ{\mathcal{I}_{\lambda}}-statistical Cauchy sequences.