Abel-type inequalities, complex numbers and Gauss-Pólya type integral inequalities

We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreasing sequences. Striking complex analogues are presented. The inequalities on the real domain are used to derive new integral inequalities related to those of Gauss-Pólya type

Abel-type inequalities, complex numbers and Gauss-Pólya type integral inequalities

We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreasing sequences. Striking complex analogues are presented. The inequalities on the real domain are used to derive new integral inequalities related to those of Gauss-Pólya type

We may not know much about the deep sea, but do we care about mining it?

1. The way we value the environment affects how we treat it. While public awareness of human impacts on the ocean is increasing, industrial activities in the deep sea are accelerating rapidly and out of sight. 2. The underlying values we hold for the environment were increasingly recognised as an important factor in environmental decision-making, and it was thus important to evaluate public values towards deep-sea environments. 3. Here, we explored people's care for the deep sea and related this to the perceived risks of seafloor mining by comparing the deep sea to three other remote environments: Antarctica, remote terrestrial environments and the Moon. 4. We conducted an online survey to investigate symbolic values, which we define as the emotions, moods and meanings an environment evokes, as an element affecting people's care for the environment. In addition, we investigated the respondent's knowledge, worldviews and the perceived environmental and societal risk of mining in these four environments. 5. We found that symbolic values shape people's environmental care and that the overall symbolic value attributed to each of the environments differs. 6. People perceived it likely that mining will take place in the deep sea, and the majority of respondents (81%) stated to care a lot or very much about human activities harming the deep sea. 7. In comparison to the other remote environments, in a general sense people cared less about the deep sea, and their self-assessed knowledge of the deep sea was lower. 8. These results suggest that it was fundamental to account for the underlying values and emotions towards the environment when evaluating the risks of human activities in remote settings. 9. Our results further highlighted the need to improve public understanding and connection with the deep sea and its role within wider society to engender deep-sea stewardship.Peer reviewe