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Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we derived the AF for the proposed transform. A bunch of important properties, including the reconstruction formula associated with the AF, are studied.

Vietnam is a key player in India's Act East Policy and is distressed due to China's overarching position in the South China Sea. China's expanding infrastructural investments in India's periphery have led to a regional security dilemma in Indian Ocean Region. India is steered to pursue opportunities to counter China in the latter's periphery, to which Vietnam fits as an apt ally. Hence, this paper examines the heightened need for realigning India's Vietnam policy in line with United Nations Sustainable Development Goals and explains how bilateral cooperation through sustainable trade, renewable energy production, and green investments can offer a 'counter' to Chinese expansion in Indo-Pacific and its Belt and Road Initiative. This paper uses the theoretical framework of Balance of Power to enumerate how geostrategic policy decisions in India-Vietnam bilateral relations can create a 'counterbalance' to the Chinese investments in India's neighborhood, especially in Pakistan., Author(s): R. S. Aswani [sup.1] , Shambhu Sajith [sup.2] , Mohammad Younus Bhat [sup.3] Author Affiliations: (1) grid.444415.4, 0000 0004 1759 0860, School for Life, University of Petroleum and Energy [...]

The free metaplectic transformation (FMT) is an n$$ n $$‐dimensional linear canonical transform. This transform is much useful, especially in multidimensional signal processing and applications. In this paper, our aim is to achieve an efficient time‐frequency representation of higher‐dimensional nonstationary signals by introducing the novel free metaplectic wave packet transform (FM‐WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$, based on the elegant convolution structure associated with the free metaplectic transforms. The FM‐WPT preserves the properties of classical wave packet transform (WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$ and has better mathematical properties. Further, the validity of the proposed transform is demonstrated via a lucid example. The preliminary analysis encompasses the derivation of fundamental properties of the novel FM‐WPT, including boundedness, reconstruction formula, Moyal's formula, and the reproducing kernel. To extend the scope of the study, we formulate several uncertainty inequalities, including Lieb's inequality, Pitt's inequality, logarithmic inequality, Heisenberg's uncertainty inequality, and Nazarov's uncertainty inequality for the proposed transform. [ABSTRACT FROM AUTHOR]

The present article establishes a novel transform known as Clifford‐valued linear canonical wavelet transform which is intended to represent n$$ n $$‐dimensional Clifford‐valued signals at various scales, locations, and orientations. The suggested transform is capable of representing signals in the Clifford domain in addition to inheriting the characteristics of the Clifford wavelet transform. In the beginning, we demonstrate the proposed transform by the help of n$$ n $$‐dimensional difference of Gaussian wavelets. We then establish the fundamental properties of the proposed transform like Parseval's formula, inversion formula, and characterization of its range using Clifford linear canonical transform and its convolution. To conclude our work, we derive an analog of Heisenberg's and local uncertainty inequalities for the proposed transform. [ABSTRACT FROM AUTHOR]

Forest fires release harmful pollutants, endangering public health and incurring substantial healthcare costs. This study empirically investigates the environment‐health‐economy relationship, utilizing a robust MM‐QR approach. Findings divulge that economic growth, urbanization, and tourism drive healthcare expenditure, while environmental factors like forest fires, resource depletion, species extinction, and environmental policy stringency also increase health spending. Conversely, renewable energy consumption lowers healthcare costs, while coal extraction raises them. Empirical estimates reveal that 1% increase in forest fires raises health spending by 0.03%−0.08%, socioeconomic indicators by 0.01%−1.07%, and environmental factors by 0.03%−3.74%. Conversely, a 1% rise in renewable energy usage cuts healthcare expenses by 0.06%−0.19%. This study underscores the urgency of addressing environmental degradation, especially forest fires, to mitigate their impacts on human well‐being. [ABSTRACT FROM AUTHOR]

This study explores the concept of residual entropy as an alternative approach to traditional entropy measures. The field of information theory, built upon Shannon's entropy, has been instrumental in understanding the dynamics of systems. However, existing literature has recognized the limitations of applying traditional entropy measures to systems that have already been in existence for a certain duration. This study delves into the concept of residual entropy, acknowledging the need for a more suitable approach for such systems. Specifically, we investigate the characteristics of residual entropy using a quantile-based framework. By deriving the quantile residual entropy function for various lifetime models, we gain insights into the reordering and ageing phenomena captured by the quantile version of the residual entropy equation. Our findings contribute to an enhanced understanding of residual entropy and provide a novel perspective on analyzing and interpreting the behavior of established systems. [ABSTRACT FROM AUTHOR]

The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT. [ABSTRACT FROM AUTHOR]

This study aims to determine the potential for improving regional cooperation and clean energy generation in the South China Sea (SCS) through Offshore Wind Energy (OWE). The literature review depicts the broad relationship between renewable energy and regional cooperation. The study identifies three variables-great game of geopolitics, geo-economics, and NEO politics- to arrive at a concept of wind-blindness. It refers to the attempt (of the countries involved) to downplay the existing wind resources and avert attention from them to safeguard the region's strategic military importance, existing trade routes, and rich availability of marine resources. Addressing these concerns could strengthen cooperation between the claimant states for technology, knowledge, and practice sharing, to ensure a sustainable South China Sea region. China's investments in OWE in the South China Sea have the potential to meet the Sustainable Development Goals" target of cleaner, accessible, and affordable energy. Finally, the paper suggests that renewable energy development in the region can reduce the maritime transport of fossil fuels, reducing the carbon footprint. [ABSTRACT FROM AUTHOR]