Normalized positive solutions for Schrödinger equations with potentials in unbounded domains

The paper deals with the existence of positive solutions with prescribed $L2$ norm for the Schrodinger equation $$-\Delta u+\lambda u+V(x)u=|u|{p-2}u,\quad u\in H1_0(\Omega),\quad\int_\Omega u2{\rm d}\,x=\rho2,\quad\lambda\in\mathbb{R},$$ where $\Omega =\mathbb {R}N$ or $\mathbb {R}N\setminus \Omega$ is a compact set, $\rho >0$, $V\ge 0$ (also $V\equiv 0$ is allowed), $p\in (2,2+\frac 4 N)$. The existence of a positive solution $\bar u$ is proved when $V$ verifies a suitable decay assumption (D?), or if $\|V\|_{Lq}$ is small, for some $q\ge \frac N2$ ($q>1$ if $N=2$). No smallness assumption on $V$ is required if the decay assumption (D?) is fulfilled. There are no assumptions on the size of $\mathbb {R}N\setminus \Omega$. The solution $\bar u$ is a bound state and no ground state solution exists, up to the autonomous case $V\equiv 0$ and $\Omega =\mathbb {R}N$

The unexpected land use: rain-fed agriculture in drylands

Although excluded from most maps of current and past land use, dryland rain-fed (non-irrigated) agriculture has been and is pivotal to enhance resilience of human communities, and understand land-atmosphere interactions and regional climate in many parts of the world

Adaptation to Variable Environments, Resilience to Climate Change: Investigating land, water and settlement in Indus northwest India

This paper explores the nature and dynamics of adaptation and resilience in the face of a diverse and varied environmental and ecological context using the case study of South Asia’s Indus Civilization (ca. 3000–1300 BC). Most early complex societies developed in regions where the climatic parameters faced by ancient subsistence farmers were varied but rain falls primarily in one season. In contrast, the Indus Civilization developed in a specific environmental context that spanned a very distinct environmental threshold, where winter and summer rainfall systems overlap. There is now evidence to show that this region was directly subject to climate change during the period when the Indus Civilization was at its height (ca. 2500–1900 BC). The Indus Civilization, therefore, provides a unique opportunity to understand how an ancient society coped with diverse and varied ecologies and change in the fundamental environmental parameters. This paper integrates research carried out as part of the Land, Water and Settlement project in northwest India between 2007 and 2014. Although coming from only one of the regions occupied by Indus populations, these data necessitate the reconsideration of several prevailing views about the Indus Civilization as a whole and invigorate discussion about human-environment interactions and their relationship to processes of cultural transformation.UKIERI, NERC, AHRC, British Academy, McDonald Institut

Global overview of the management of acute cholecystitis during the COVID-19 pandemic (CHOLECOVID study)

Background: This study provides a global overview of the management of patients with acute cholecystitis during the initial phase of the COVID-19 pandemic. Methods: CHOLECOVID is an international, multicentre, observational comparative study of patients admitted to hospital with acute cholecystitis during the COVID-19 pandemic. Data on management were collected for a 2-month study interval coincident with the WHO declaration of the SARS-CoV-2 pandemic and compared with an equivalent pre-pandemic time interval. Mediation analysis examined the influence of SARS-COV-2 infection on 30-day mortality. Results: This study collected data on 9783 patients with acute cholecystitis admitted to 247 hospitals across the world. The pandemic was associated with reduced availability of surgical workforce and operating facilities globally, a significant shift to worse severity of disease, and increased use of conservative management. There was a reduction (both absolute and proportionate) in the number of patients undergoing cholecystectomy from 3095 patients (56.2 per cent) pre-pandemic to 1998 patients (46.2 per cent) during the pandemic but there was no difference in 30-day all-cause mortality after cholecystectomy comparing the pre-pandemic interval with the pandemic (13 patients (0.4 per cent) pre-pandemic to 13 patients (0.6 per cent) pandemic; P = 0.355). In mediation analysis, an admission with acute cholecystitis during the pandemic was associated with a non-significant increased risk of death (OR 1.29, 95 per cent c.i. 0.93 to 1.79, P = 0.121). Conclusion: CHOLECOVID provides a unique overview of the treatment of patients with cholecystitis across the globe during the first months of the SARS-CoV-2 pandemic. The study highlights the need for system resilience in retention of elective surgical activity. Cholecystectomy was associated with a low risk of mortality and deferral of treatment results in an increase in avoidable morbidity that represents the non-COVID cost of this pandemic

Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains

The paper concerns with positive solutions of problems of the type $-Delta u+a(x), u=u^{p-1}+arepsilon u^{2^*-1}$ in $OmegasubseteqR^N$, $Nge 3$, $2^*={2Nover N-2}$, 2<2^*. Here $Omega$ can be an exterior domain, i.e. $R^NsetminusOmega$ is bounded, or the whole of $R^N$. The potential $ain L^{N/2}_{loc}(R^N)$ is assumed to be strictly positive and such that there exists lim_{|x| oinfty}a(x):=a_infty>0. First, some existence results of ground state solutions are proved. Then the case $a(x)ge a_infty$ is considered, with $a(x) otequiv a_infty$ or $Omega eqR^N$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small $e$

Infinitely many solutions for polyharmonic elliptic problems with broken symmetries

We get the existence of infinitely many solutions for a class of polyharmonic elliptic problems with broken symmetrie

The end of the Holocene Humid Period in the central Sahara and Thar deserts: societal collapses or new opportunities?

Climatic Optimum (ca. 12–5 ka BP), in its local, monsoon-tuned variants of the African Humid Period (DeMenocal et al. 2000; Gasse 2000) and the period of strong Asian southwest (or summer) monsoon (Dixit et al. 2014), is one of the best-studied climatic phases of the Holocene. Yet the ensuing trend towards aridity, the surface processes shaping the present-day arid lands and the cultural responses to these are still debated. Human reactions to arid environmental conditions have been sometimes described in terms of demographic decrease (e.g. Manning and Timpson 2014) and as driving socio-cultural complexity (e.g. Kuper and Kröpelin 2006). These two concepts, although apparently conflicting, are not mutually exclusive. The onset of arid conditions can lead to demographic decrease or the rearrangement of the population around important or secure resources. In turn, this can favor the adoption of different strategies to cope with the new climatic conditions, leading to augmented social stratification and complexity, and eventually to the emergence of hierarchical state-like entities.Peer reviewe

Expanding our frame of reference: cross-cultural modeling for Ethnoarchaeology

Theoretical approaches in ethnoarchaeology have been generally characterized by discourses around analogical reasoning and its implications for archaeology. On the contrary, ethnoarchaeological fieldwork has traditionally been context-specific, and oriented toward certain issues (e.g. the spatial patterning of setdemems and items, the production and circulation of artifacts, the symbolic domain, etc). In this presentation, we tackle the absence of crosscultural ethnoarchaeological data in major ethnographic databases. We explore the possibility of adding to these databascs and use ethnoarchaeological cross-cultural studies to devise generalised models that have unambiguous material correlates and can thus be used to investigate human behaviour in the past.Peer Reviewe