In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.

Distributed Energy Resources (DERs), such as solar photovoltaic (PV) systems, wind turbines, and energy storage systems, offer many benefits, including increased energy efficiency, sustainability, and grid reliability. However, their integration into the smart grid also introduces new vulnerabilities to cyber threats. The smart grid is becoming more digitalized, with advanced technologies like Internet of Things (IoT) devices, communication networks, and automation systems that enable the integration of DER systems. While this enhances grid efficiency and control, it creates more entry points for attackers and thus expands the attack surface for potential cyber threats. Protecting DERs from cyberattacks is crucial to maintaining the overall reliability, security, and privacy of the smart grid. The adopted cybersecurity strategies should not only address current threats but also anticipate future dangers. This requires ongoing risk assessments, staying updated on emerging threats, and being prepared to adapt cybersecurity measures accordingly. This paper highlights some critical points regarding the importance of cybersecurity for Distributed Energy Resources (DERs) and the evolving landscape of the smart grid. This research study shows that there is need for a proactive and adaptable cybersecurity approach that encompasses prevention, detection, response, and recovery to safeguard these critical energy systems against cyber threats, both today and in the future. This work serves as a valuable tool in enhancing the cybersecurity posture of utilities and grid-connected DER owners and operators. It allows them to make informed decisions, protect critical infrastructure, and ensure the reliability and security of grid-connected DER systems in an evolving energy landscape.

The search for the development of nanostructured materials has led to the study of the properties of their precursors. For the production of nanofibers by the electrospinning process, it is necessary to determine the rheological parameters of the precursor solutions. Since these properties can be influenced by the processing variables and chemical composition of the polymer, this study aims to elucidate the effect of the addition of vinyl monomers in the formulation of nanofibers based on polyacrylonitrile and to determine the optimal parameters for the production of the precursor polymer solution. The effects of temperature and addition of vinyl monomers were evaluated by rheometry, from the analysis of the variation of the viscosity of the solutions, and by microscopy, the morphology of the nanofibers produced. It was observed that the increase in the temperature used to produce the solutions improves the fibers’ properties. Still, there is a relationship between the time of exposure of the polymeric solution to the temperature and the homogeneity of the fibers, which cannot exceed 45 min. The addition of vinyl monomers, to produce PAN-PVA co-polymeric fibers, increases the conductivity and reduces the viscosity of the solutions, resulting in more refined and homogeneous fibers.

Researchers from all over the world have been working tirelessly to combat the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) COVID-19 pandemic since the World Health Organization (WHO) proclaimed it to be a pandemic in 2019. Expanding testing capacities, creating efficient medications, and creating safe and efficient COVID-19 (SARS CoV-2) vaccinations that provide the human body with long-lasting protection are a few tactics that need to be investigated. In clinical studies, drug delivery techniques, including nanoparticles, have been used since the early 1990s. Since then, as technology has advanced and the need for improved medication delivery has increased, the field of nanomedicine has recently seen significant development. PNPs, or polymeric nanoparticles, are solid particles or particulate dispersions that range in size from 10 to 1000 nm, and their ability to efficiently deliver therapeutics to specific targets makes them ideal drug carriers. This review article discusses the many polymeric nanoparticle (PNP) platforms developed to counteract the recent COVID-19 pandemic-related severe acute respiratory syndrome coronavirus (SARS-CoV-2). The primary subjects of this article are the size, shape, cytotoxicity, and release mechanism of each nanoparticle. The two kinds of preparation methods in the synthesis of polymeric nanoparticles have been discussed: the first group uses premade polymers, while the other group depends on the direct polymerization of monomers. A few of the PNPs that have been utilized to combat previous viral outbreaks against SARS-CoV-2 are also covered.

This paper highlights the opportunities as well as challenges posed for Bangladesh by the Belt and Road Initiative (BRI) of China. BRI is being considered as the most expensive project ever initiated connecting more than half of the world population from Asia, Europe and Africa. For writing this paper, the authors utilized published sources such as journal articles, newspaper articles and web-based information published from 2013 to 2024. The article proposes that although the involvement of Bangladesh in the BRI is not absolutely free of challenges, it can serve the ultimate national interest through greater connectivity with other countries, increased volume of trade and economic activities and socio-cultural exchange. Although, as the originator and major contributor of the BRI, China will be the principal benefiter, other partner countries can also attain considerable benefits out of this historical mega scheme through the application of appropriate vision and strategic implementation. This paper has highlighted those benefits/opportunities and challenges for Bangladesh that can be beneficial for upcoming research projects particularity aimed at development studies, political economy and international relations. On the other hand, based on the arguments made on this paper, policymakers and businessmen can formulate their best policies as well as trading strategies with mutual benefits for all the stakeholders involved.

This paper provides a comprehensive review of equity trading simulators, focusing on their performance in assuring pre-trade compliance and portfolio investment management. A systematic search was conducted that covered the period of January 2000 to May 2023 and used keywords related to equity trade simulators, portfolio management, pre-trade compliance, online trading, and artificial intelligence. Studies demonstrating the use of simulators and online platforms specific to portfolio investment management, written in English, and matching the specified query were included. Abstracts, commentaries, editorials, and studies unrelated to finance and investments were excluded. The data extraction process included data related to challenges in modern portfolio trading, online stock trading strategies, the utilization of deep learning, the features of equity trade simulators, and examples of equity trade simulators. A total of 32 studies were included in the systematic review and were approved for qualitative analysis. The challenges identified for portfolio trading included the subjective nature of the inputs, variations in the return distributions, the complexity of blending different investments, considerations of liquidity, trading illiquid securities, optimal portfolio execution, clustering and classification, the handling of special trading days, the real-time pricing of derivatives, and transaction cost models (TCMs). Portfolio optimization techniques have evolved to maximize portfolio returns and minimize risk through optimal asset allocation. Equity trade simulators have become vital tools for portfolio managers, enabling them to assess investment strategies, ensure pre-trade compliance, and mitigate risks. Through simulations, portfolio managers can test investment scenarios, identify potential hazards, and improve their decision-making process.