HJB Equations and Stochastic Control on Half-Spaces of Hilbert Spaces

In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces to the case where the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear HJB equation. Our main goal is to establish the existence and the uniqueness of solutions to such HJB equations, which are continuously differentiable in the space variable. We also provide an application of our results to an exit-time optimal control problem, and we show that the corresponding value function is the unique solution to a semilinear HJB equation, possessing sufficient regularity to express the optimal control in feedback form. Finally, we give an illustrative example

A simple planning problem for COVID-19 lockdown: a dynamic programming approach

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach

Shrub Cover and Soil Moisture Affect Taxus baccata L. Regeneration at Its Southern Range

The effect of key ecological and anthropic factors on the recruitment of the common yew (Taxus baccata L.) in Sardinia (Italy) has been analyzed. After bibliographic and cartographic research, followed by field surveys, we found 232 sites where yew grows in Sardinia (as opposed to 69 previously reported in the literature). Among them, we selected 40 sites, located in 14 different mountain chains, characterized by a number of individuals ranging from 11 to 836 adult yews with an average diameter at breast height (DBH) from 13 to 130 cm. By means of generalized linear modeling, we investigated and weighted the effect of ecological, structural, and anthropic factors on the amount of T. baccata recruitment. Our analyses showed that stand recruitment was positively correlated to shrub cover and soil moisture. In particular, shrub cover had a stronger effect, clearly showing that a thicker shrub layer, both bushy and/or spiny, corresponded to a higher number of yew seedlings and saplings. Secondarily, moister sites had a higher number of seedlings and saplings, showing that habitat suitability improved with higher humidity. On the contrary, recruitment was negatively correlated to browsing (both from livestock and wild animals). Our data confirm that the presence of a protective layer of shrubs is a crucial factor for seedling and sapling survival, mostly in relation to protection from summer drought and the browsing of large herbivores. Finally, guidelines for the conservation and restoration of T. baccata communities, referred to as the EU priority habitat 9580* (Mediterranean Taxus baccata woods), have been outlined

New national and regional Annex I Habitat records: from # 21 to #25

New Italian data on the distribution of the Annex I Habitats 3170*, 6110*, 91E0*, 9320, 9330 are reported in this contribution. Specifically, one new occurrence in Natura 2000 sites is presented and six new cells are added in the European Environment Agency 10 km × 10 km reference grid. The new data refer to the Italian administrative regions of Sardinia, Sicily and Umbria

Contribution to a new vascular flora of Sardinia (Italy): I (1-30)

In the context of creating a new, updated, and revised vascular flora of Sardinia, this work contributes new data on the distribution of various taxa in the island. These include both native and alien taxa, which are characterized by their rarity, limited recognition, hytogeographical significance, potential issues, or novelty to Sardinia. These updates mostly result from floristic research primarily conducted in north Sardinia, with several discoveries in other sectors of the island. The first report of Convolvulus sabatius subsp. mauritanicus, Cyperus brevifolioides (naturalized) and Brachychiton populneus (casual alien) in Sardinia is documented here. Moreover, this study includes new distributional data for 27 taxa, some of which required confirmation. Notably, Trifolium clusii, previously considered doubtful in recent years, along with Fuirena pubescens and Silene inaperta, which were indicated for the southern part of Sardinia over thirty years ago and have not been reported elsewhere since. For others, an expansion or a better definition of their distribution range within the island is documented, as in the case of Chloris gayana, Digitaria ciliaris, Eragrostis curvula, Paraserianthes lophantha, Sporobolus indicus (naturalized alien species), Asparagus asparagoides, Cenchrus setaceus, Eclipta prostrata, Halophila stipulacea (invasive alien species), Allium sardoum, A. savii, Anthyllis barba-jovis, Asplenium marinum, Bellevalia romana, Butomus umbellatus, Cladium mariscus, Dianthus sardous, Dysphania botrys, Jacobaea maritima subsp. maritima, Leersia oryzoides, Nepeta foliosa, Nuphar lutea, Spirodela polyrrhiza, Utricularia australis (rare native)

Mediterranean plant germination reports – 5

This is the fifth issue of the series of germination reports from Mediterranean areas (sensu Med-Checklist). It comprises germination protocols for 18 taxa: Hieracium and Pilosella from South Italy by Di Gristina & al. (Nos. 103-106); Genista from Sardinia by Deplano & al. (No. 107); Antirrhinum, Anthyllis, Digitalis, Echium, Jasione, Nothoscordum, Silene and Verbascum by Martínez-Oliver & al. (Nos. 108-116); Dianthus, Helichrysum and Silene from Sicily by Scafidi & Salmeri (Nos. 117-120)

Global and Regional IUCN Red List Assessments: 2

In this contribution the conservation status assessment of six plant species according to IUCN categories and criteria are presented. It includes the assessment at global level of Charybdis glaucophylla Bacch., Brullo, D'Emerico, Pontec. & Salmeri, Euphorbia nicaeensis All. subsp. japygica (Ten.) Arcang., Hieracium australe Fr. subsp. australe, Limonium multiforme Pignatti, Onosma helvetica Boiss. em. Teppner subsp. lucana (Lacaita) Peruzzi, Aquaro & Cesca and the assessment at national level (Italy) of Lathyrus laxiflorus (Desf.) Kuntze subsp. laxiflorus

Notulae to the Italian alien vascular flora: 16

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records and status changes from casual to naturalized for Italy or for Italian administrative regions. Nomenclatural and distribution updates, published elsewhere, and corrections are provided as supplementary material

Notulae to the Italian native vascular flora: 9

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations, exclusions, and status changes to the Italian administrative regions. Two new combinations are proposed. Nomenclatural and distribution updates, published elsewhere, and corrigenda are provided as Suppl. material 1

Notulae to the Italian native vascular flora: 9

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations, exclusions, and status changes to the Italian administrative regions. Two new combinations are proposed. Nomenclatural and distribution updates, published elsewhere, and corrigenda are provided as Suppl. material