It establishes a regularity criterion for non-Newtonian fluids in $\mathbb{R}^3$ in terms of the weighted gradient of the velocity field, based on the Caffarelli--Kohn--Nirenberg inequality.
Chiara Fraticelli, Claudio Sillero-Zubiri, Herwig Leirs
et al.
Abstract Lions are threatened, especially in West and Central Africa, with conflict as key factor, especially outside core protected areas. Using GPS satellite collars, we studied the movement of 15 lions in Chad’s Greater Zakouma Ecosystem (GZE), and specifically its core area Zakouma National Park. We analysed their home range and core range sizes, and compared movement patterns during the wet and dry seasons, between 2020 and 2023. In the dry season, lions in the eastern part of Zakouma National Park mainly ranged within the boundaries of the park, where wild prey concentrated around remaining waterholes. In the wet season lions shifted their home ranges to areas outside the park, resulting in very large total home range sizes. Outside the park, lions exhibited increased nocturnal activity and travelled over considerably greater distances, however this strategy did not prevent human-lion conflict. We conclude that lions in the GZE regularly use areas outside the national park, suggesting that conservation efforts within the park alone are insufficient for the species’ conservation. Mitigating conflicts in surrounding community areas is crucial to prevent a population decline and ensure landscape connectivity.
In this paper, we shall study existence of weak solutions to complex Hessian equations. With appropriate assumptions, it is possible to obtain weak solutions in pluripotential sense.
In this paper, we establish an interior $C^2$ estimate for the Hessian quotient equation $\left(\frac{σ_3}{σ_1}\right)(D^2u)=f$ in dimension three. A crucial ingredient in our proof is a Jacobi inequality.
It is shown that for any real gas in chemical equilibrium, the convexity proposed by Lax isequivalent to the concavity of the entropy considered as thermodynamic potential and thepositivity of temperature.
It has been more than a decade since I completed my own participation in a public archaeology project at Rogem Gannim, in West Jerusalem (Natasha Dudinski, “The Past on our Doorstep,” https://www.youtube.com/watch?v=ef3fPcrB11c); since then, in the role of an archaeological activist and advocate, I have observed the progress of public archaeology in Israel and abroad and participated in the local and global dialogue (Clark and Horning 2019), without initiating new fieldwork. This brief note, though looking toward the future as requested by the editors, is therefore retrospective in origin, rather than being a missive from the front lines.
We prove the existence of heteroclinic traveling waves (kinks) in an infinite array of weakly coupled pendula. Our approach is to apply a perturbation argument from the anti-continuum limit.
This Introduction to AP’s third special issue seeks to provide context and rationale to the study of ‘public mortuary archaeology’ before reviewing the development of the volume. Building on the presentations of the first Public Archaeology Twitter Conference of April 2017, these articles comprise a wide range of original analyses reflecting on the public archaeology of death, including evaluations of fieldwork contexts, churches and museums. These articles are joined by discussions of the digital dimensions to public mortuary archaeology, an appraisal of ancient and modern DNA research as public mortuary archaeology, and the relationship between mortuary archaeology and palliative care. Together, the articles constitute the state of current thinking on the public archaeology of death, burial and commemoration.
It is shown that the "tangential" electric and magnetic fields, in the Glassey-Strauss representation formulas, are in fact bounded in $L^\infty_{{\rm loc},\,t} L^{2+δ}_x$ for some $δ>0$.
There is often a disconnect between archaeology and the education system. Archaeologists, as well as educators, can use many aspects of archaeology to help teach children about science and history in multi-disciplinary ways. However, archaeology is not included in the curriculum of the United Kingdom.The role of commercial archaeology is also essential in this, because they also have a responsibility of informing local communities about the archaeology they are doing. By making strides to include archaeology in the classroom by educators and continuing it in archaeological practice by archaeologists, children will be better informed about what archaeology is and how it works. Also, teaching children about archaeology can help to provide them with not only a greater understanding and appreciation for archaeology and but also its application of the scientific method outside of the typical spectrum of science courses.
We prove the local-in-time well-posedness and the mass and energy conservation laws for a 3d cubic nonlinear Schroedinger equation with a real-valued potential.
We study a Dirichlet problem for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side. We will show that the right-hand side has some regularizing effects on the solutions, even if it is singular.