Narrow Results

The paper reviews some parts of classical potential theory with applications to two-dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the vortices are kept fixed, but the dynamics is different in the case of free vortices. Starting from Euler’s and Bernoulli’s equations we derive these laws. Letting the number of vortices tend to infinity leads in the limit to considerations of equilibrium distributions, capacity, harmonic measure and many other notions in potential theory. In particular various kinds of Green functions have a central role in the paper, and we make a distinction between electrostatic and hydrodynamic Green functions. We also consider the corresponding concepts in the case of closed Riemann surfaces provided with a metric. From a canonically defined monopole Green function we rederive much of the classical theory of harmonic and analytic forms on Riemann surfaces. In the final section of the paper we return to the planar case, which then reappears in the form of a symmetric Riemann surface, the Schottky double. Bergman kernels, electrostatic and hydrodynamic, come up naturally as well as other kernels, and associated to the Green function there is a certain Robin function which is important for vortex motion, and which also relates to capacity functions in classical potential theory.

This paper investigates the multi-dimensional risk spillover effects of carbon markets with energy, non-energy commodity and stock markets in China before and after the COVID-19 outbreak, through the DY network with GARCHSK-VaR method. The empirical results denote that the total bidirectional risk spillovers of carbon markets become larger after the COVID-19 outbreak than before the COVID-19 outbreak. Interestingly, in both periods, energy is the largest risk contributor to carbon markets, while carbon markets become the net risk contributors to stock markets under COVID-19. Furthermore, compared with Guangdong pilot, the impacts of Hubei pilot on other markets are stronger in both periods. Finally, the dynamic risk spillover effects have obvious differences between before and after the COVID-19 outbreak.

Regardless of the state of matter, such as solids, liquids, and gases, the smaller the matter size from bulk to nano-scale, especially in the quantum region, the more rapid is the energy increase. To this end, this study introduces the concept of a group system, in which atoms behave as one, and this system is reinterpreted as that comprising temperature–entropy (TS) energy in thermodynamic data. Based on this concept, water was passed through various mesh-like dissolved tubes, where the size and energy of the water group system were observed to change. Thereafter, as the scale and number of the meshes increased, the ozone, chlorine, and oxygen constituents, which are closely related to sterilization and washing, are generated, changing the basic water composition. Thus, this nano-size impact is not limited to solids and could facilitate in revolutionizing the future applications in fluids.

Let ${ℛ}$ be commutative ring and $Z^{\ast }({ℛ})$ be the set of all non-zero zero divisors of ${ℛ}$. Then $\mathrm{\Gamma }({ℛ})$ is said to be the zero divisor graph if and only if $a\cdot b=0$ where $a,b\in V(\mathrm{\Gamma }({ℛ}))$ and $(a,b)\in E(\mathrm{\Gamma }({ℛ}))$. Graph energy ${ℰ}(\mathrm{\Gamma }({ℛ}))$ is defined as the sum of the absolute eigenvalues of the adjacency matrix ${ℳ}(\mathrm{\Gamma }({ℛ}))$, then ${ℰ}(\mathrm{\Gamma }({ℛ}))={\sum }_{i=1}^n\left|{\lambda }_i\right|$. Wiener index $W(\mathrm{\Gamma }({ℛ}))$ is defined as the sum of all distance between pairs of vertices $a$ and $b$, then $W(\mathrm{\Gamma }({ℛ}))={\sum }_{a,b\in V(\mathrm{\Gamma }({ℛ}))}d(a,b)$. In this paper, we compute the graph energy from the adjacency matrix of the zero divisor graph and the Wiener index from the zero divisor graph associated with commutative rings.

This paper provides a detailed, cross-model analysis and discussion of the implications of carbon tax scenarios on changes in sectoral output, energy production and consumption and the competitiveness of the United States’ economy. Our analysis focuses on the broad patterns apparent across models in both qualitative and quantitative terms at the sector level, with a focus on energy-intensive, trade-exposed sectors. We identify how variations in carbon tax trajectories and different options for using the revenue from the tax drive these results.

About 140 countries have announced or are considering net zero targets. To explore the implications of such targets, we apply an integrated earth system–economic model to investigate illustrative net zero emissions scenarios. Given the technologies as characterized in our modeling framework, we find that with net zero targets afforestation in earlier years and biomass energy with carbon capture and storage (BECCS) technology in later years are important negative emissions technologies, allowing continued emissions from hard-to-reduce sectors and sources. With the entire world achieving net zero by 2050 a very rapid scale-up of BECCS is required, increasing mitigation costs through mid-century substantially, compared with a scenario where some countries achieve net zero by 2050 while others continue some emissions in the latter half of the century. The scenarios slightly overshoot 1.5^∘C at mid-century but are at or below 1.5^∘C by 2100 with median climate response. Accounting for climate uncertainty, global achievement of net zero by 2050 essentially guarantees that the 1.5^∘C target will be achieved, compared to having a 50–50 chance in the scenario without net zero. This indicates a tradeoff between policy costs and likelihood of achieving 1.5^∘C.

Based on the multi-regional input-output framework, this paper analyzed the labor and energy transfer embodied in interregional trade in China. Meanwhile, through estimating the energy intensity per unit of labor embodied in final products in each region, this study examines whether the empirical results are consistent with the theoretical hypothesis and provides relevant explanations and industrial development suggestions. Results show that east coastal region and central region are the two main participants in interregional trade. As for the labor embodied in trade, east coastal region is the largest exporter of embodied labor, though it has the highest wage among eight regions; in contrast, north coastal and southwestern region, with relatively low wage, are the two largest importer of embodied labor. As for the energy embodied in trade, northwestern region is the largest exporter of embodied energy. Further analysis indicates that the energy intensity per unit of labor in region with relatively low GRP (such as northwestern region) is the highest, whereas those in Beijing-Tianjin Region and south coastal region (with relatively high GRP) are the lowest. By analyzing the Revealed Comparative Advantage in each region, the paper finds that the main reason for this inconsistency lies in the industrial structure in northwestern and north coastal region, which are highly dependent in primary industries. Improving the infrastructure and upgrading industrial structure are important steps for these regions to transform the extensive growth mode.

The China-Pakistan Economic Corridor (CPEC) offers a massive platform for China and Pakistan to promote regional connectivity, trade growth, and infrastructure development. Pakistan views CPEC not only as an infrastructure and economic development program as well as a key initiative with wide-ranging implications for the country’s domestic economy and social makeup, but also a potential “game changer” in the regional situation. However, this project also faces grave internal and external challenges, such as route controversy, militancy, religious extremism, competing narratives, media propaganda, debt-trap accusation, and synergy of institutions. To make CPEC a sustainable project that benefits Pakistan and the whole of South Asia in the long run, both the Chinese and Pakistani governments need to address these challenges through greater transparency of the CPEC projects, as well as more consultation with all stakeholders involved, so as to ease their concerns about the profound implications of the grand project.

Based on the smallest physical constant of the product of space interval, time interval, and energy, the fractal quantum gravity (FQG) theory has demonstrated that every particle or physical system consists of these smallest units in fractal structures. The general relativity is an approximation of the FQG equation when the quantum effect is negligible, while the quantum theory is an approximation of the FQG equation when the interaction between space, time, and energy is very weak or negligible. The stationary-action principle can be derived from the FQG equation. The mass range of possibly existing elementary particles and an accelerating expansion evolution model of the universe can be obtained through the FQG equation. This FQG equation satisfied almost all the requirements of a quantum gravity theory and there is no free constant needed in the FQG theory. It looks promising that the FQG theory may offer a novel way to calculate all the free constants in the Standard Model of particle physics and general relativity.

As the world’s population continues to expand, scientists are working to address the energy needs and challenges that accompany growth with environmentally responsible approaches. Nanoscience is helping to provide solutions to energy and environmental concerns in a number of ways.

The current topic of clean air and water is often left incomplete. When we discuss cleaner cars or more regulations, we forget that none of this can genuinely be sustainable without improving our infrastructure, an objective we are mostly avoidant. With this sprouting age of technology, we have companies interject that their model is “the newest in sustainability.” Still, the systems that support production have fallen rapidly behind due to a lack of funding and push from the public. In this paper, I hope to begin a discussion on the importance of improving our energy infrastructure over the course of my lifetime. Eventually, a sprout of real change might happen to improve the lives of those around me.

The CSFS is an extension of CPFS and CPicFS. The design addresses vagueness more explicitly. It extends the real subset’s range to complex with the use of unit disc. Due to its coverage in three directions: complex membership functions, complex abstinence membership function, and complex non-membership functions, CSFS has more flexibility than CFSs, CIFSs, CPFSs, and CPicFS. It can be applied in various ways through fuzzy control. The primary objective of this study is to present CSFGS, which exhibits exceptional performance in tackling challenging problem, particularly ones that involve multiple relationships. GSs and CSFSs are combined in this concept. As a result, many problems are combined with different relations. The AM of CSFGS and degree of vertex presence have been found. The lower and upper constraints on the energy of CSFGS are derived by calculating the energy of CSFGS. Furthermore, we have provided some details regarding the LE of the ${\sigma }_J$-dominant CSFGS. We also propose the notion of isomorphic and identical ${\sigma }_J$-dominating CSFGS. Finally, we have discussed a real-world example based on temperature variation and climatic data analysis in an environment with a LE of the ${\sigma }_J$-dominant CSFGS, to demonstrate the applicability of the generated results. Also, an algorithm has been developed to clarify the fundamental workings of our application.

Using data from the 2007 Timor-Leste Living Standards Survey, this paper examines the determinants of household energy choices in Timor-Leste. The majority of households are dependent on dirty fuels such as fuelwood and kerosene for energy. Only a small fraction of households use clean energy such as electricity. Econometric results show that wealthy households, urban households, and those headed by individuals with higher levels of education are less likely to use and depend on kerosene and more likely to use and depend on electricity. While female-headed households are generally more likely to use and depend on fuelwood, richer female-headed households are more likely to use and depend on electricity. Our findings highlight the importance of ensuring an adequate supply of clean energy for all at affordable prices and of investing in education to raise awareness about the adverse impacts of using dirty fuels.

The World Nuclear Industry Report (WNISR) is an annual assessment of the status and trends in the commercial nuclear industry. The report has, for the past 15 years, monitored global construction, operation and closure of reactors and makes comparisons with the developments of renewable energy and the implications for climate change.

Arguably, to nourish or take care of the needs of all of humankind — sustainable and affordable access to clean water, safe sanitation, and clean air, together with a sufficiency of energy, food, and shelter — should be universally available. Yet, many humans do not enjoy such access or availability, even though it has been 70 years since the 1948 United Nations (UN) declaration on human rights proclaimed “that all human beings are equal, and have inherent rights.” However, only food and shelter were explicitly mentioned in the initial declaration. Others were recently added to the UN list, but not air and energy. Nevertheless, basic human needs do not have to be declared as a human right before national actions are taken. Today’s key driver is the UN 2030 Agenda, a plan to eradicate all global poverty and set the world onto a “sustainable and resilient path,” through the achievement of 17 Sustainable Development Goals (SDGs). Adopted by all UN members, the 2030 Agenda in essence, is a 21^st century version of the 1948 proclamation. The SDGs explicitly detail, or implicitly in the case of clean air, all the necessary needs for the nourishing of tomorrow. To achieve the plan will likely require, at least, changes in national cultural values, eliminating inequalities and disparities, developing more appropriate governance strategies, and meaningful technical innovation. In this chapter, these requirements are discussed against a backdrop of presently known deficiencies in global nourishment needs.