We rederive the expression of the integrated density of states for \ the sub-Laplacian on Heisenberg groups $\mathbb{H}_{n}$ by using its resolvent kernel.
In this paper, we derive the existence of solutions with small volume to the $L_p$-Gaussian Minkowski problem for $1\leq p<n$, which implies that there are at least two solutions for the $L_p$-Gaussian Minkowski problem.
We have just celebrated ten years of open access public archaeology, and now we carry on with our venture. Volume 11 brings with it a new layout and format, as well as a new timing for publication. Since our inclusion in Scopus, improving quality goes in hand with the improvement of publication time. This is why, from now on (although this year is still a transitional period), volumes will open in January and close in October, with articles being published when they are ready. We are also starting a new section for shorter articles, aimed at the reporting of projects or ideas with a more formal format than our section Points of You, which will continue to retain its op-ed style. Of course, the philosophy does not change. We want to continue to be an opportunity of wider accessibility for authors and readers, and to continue exploring the physical and thematic frontiers of the discipline.
A popular proverb states ‘Don't play with your food’. This maxim that not only concerns those of us who have the immense fortune of dedicating our working hours (and more if possible) to the noble discipline of archaeology and historical research. If anything is really clear to us, it is that Heritage (from the perspective of investigation, safeguard and management) is more than the ‘food’ of a couple of professors and four tourist guides, but of many thousands whose income depends on it essentially through tourism. In fact, tourism in Spain in 2019 before the pandemic yielded 154,487 million Euros to the economy, representing 12.4% of its GDP. In fact, dear reader, please reflect on what drives you to go on vacation? And what leads you to choose one tourist destination over another? The response is simple: diversity. It represents a search for something that is unknown where you reside, something unique and unrepeatable that is only found at a particular destination, a unique setting offering an aesthetic or gastronomic experience that otherwise would not be worth the visiting. This book under review delves precisely into the question of this diversity we seek when traveling as it is Heritage (either material or intangible, artistic, monumental, archaeological or natural) that gives an identity to each city, each community. Heritage renders them different from other neighbouring cities. From a material point of view, Heritage is what attracts tourists and, even more, from a sentimental point of view, it is what offers signs of identity to locals. Thus in the end we are not only talking about ‘things to eat’.
We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality itself and not the actual flow, allowing for somewhat robust and self-contained proofs.
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.
We give sharp limiting case Hardy inequalities on the sphere $\mathbb{S}^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\setminus\{0\}$. The singularity of the problem is related to the geodesic distance from a point on the sphere.
Public archaeology increases public awareness of archaeological issues and their practical applications to modern social concerns. Classroom visits, hands-on activities, site tours, and other events give archaeologists the opportunity to engage the public and transfer knowledge through face-to-face interaction. However, engagement ends at the conclusion of the event, leaving the audience with an incomplete understanding of the subject. Twitter, a social media application, transcends these spatial and temporal limitations by allowing sustained multi-directional communication among archaeologists, their audience and others who never attended the original event. However, there are problems with assessing the success of public archaeology projects and the presentation format differs dramatically from traditional forms of publication.
In this work, we prove a weak Harnack estimate for the weak supersolutions to the porous medium equation. The proof is based on a priori estimates for the supersolutions and measure theoretical arguments.
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
In $\mathbb{R}^d$, the characterization of the \mbox{lack of compactness of the continuous Sobolev injection $ \mathring{H}^s \hookrightarrow L^p $}, with $ \displaystyle{\frac{s}{d} + \frac{1}{p} = \frac{1}{2}} $ and $\displaystyle{0
In this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in Minkowski space.
We consider the stationary Keller-Segel system from chemotaxis in a ball and we show the existence of a solution concentrating at the boundary of the ball.