A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws

We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem $$\begin{cases} u_t+[\varphi(u)]_x=0 & \text{in } \mathbb{R}\times (0,T) \\ u=u_0\ge 0 &\text{in } \mathbb{R}\times \{0\}, \end{cases}$$ where $u_0$ a positive Radon measure whose singular part is a finite superposition of Dirac masses, and $\varphi\in C^2([0,\infty))$ is bounded. The novelty of the paper is the introduction of a compatibility condition which, combined with standard entropy conditions, guarantees uniqueness

On a semilinear elliptic equation with inverse square potential

On a semilinear elliptic equation with inverse square potentia

Measure-Valued solutions to a nonlinear Fourth-Order regularization of forward-backward parabolic equations

We introduce and analyze a new, nonlinear fourth-order regularization of forwardbackward parabolic equations. In one space dimension, under general assumptions on the potentials, which include those of Perona--Malik type, we prove existence of Radon measure-valued solutions under both natural and essential boundary conditions. If the decay at infinity of the nonlinearities is sufficiently fast, we also exhibit examples of local solutions whose atomic part arises and/or persists (in contrast to the linear fourth-order regularization) and even disappears within finite time (in contrast to pseudoparabolic regularizations)

Radon measure-valued solutions of first order scalar conservation laws

Abstract We study nonnegative solutions of the Cauchy problem \left\{\begin{aligned} &\displaystyle\partial_{t}u+\partial_{x}[\varphi(u)]=0&% &\displaystyle\phantom{}\text{in }\mathbb{R}\times(0,T),\\ &\displaystyle u=u_{0}\geq 0&&\displaystyle\phantom{}\text{in }\mathbb{R}% \times\{0\},\end{aligned}\right. where {u_{0}} is a Radon measure and {\varphi\colon[0,\infty)\mapsto\mathbb{R}} is a globally Lipschitz continuous function. We construct suitably defined entropy solutions in the space of Radon measures. Under some additional conditions on φ, we prove their uniqueness if the singular part of {u_{0}} is a finite superposition of Dirac masses. Regarding the behavior of φ at infinity, we give criteria to distinguish two cases: either all solutions are function-valued for positive times (an instantaneous regularizing effect), or the singular parts of certain solutions persist until some positive waiting time (in the linear case {\varphi(u)=u} this happens for all times). In the latter case, we describe the evolution of the singular parts

Role of Neutrophil-to-Lymphocyte Ratio (NLR) in Patients with Mycosis Fungoides

background: the neutrophil/lymphocyte ratio (NLR) at baseline has been demonstrated to correlate with higher stages of disease and to be a prognostic factor in numerous cancers. however, its function as a prognostic factor for mycosis fungoides (MF) has not been yet clarified. objective: our work aimed to assess the association of the NLR with different stages of MF and to outline whether higher values of this marker are related to a more aggressive MF.methods: we retrospectively calculated the NLRs in 302 MF patients at the moment of diagnosis. the NLR was obtained using the complete blood count values.results: the median NLR among patients with early stage disease (low-grade IA-IB-IIA) was 1.88, while the median NLR for patients with high-grade MF (IIB-IIIA-IIIB) was 2.64. statistical analysis showed positive associations of advanced MF stages with NLRs higher than 2.3. conclusions: our analysis demonstrates that the NLR represents a cheap and easily available parameter functioning as a marker for advanced MF. this might guide physicians in recognizing patients with advanced stages of disease requiring a strict follow-up or an early treatment

An overview of the Italian forest biodiversity and its conservation level, based on the first outcomes of the 4th Habitat Report ex-Art. 17

In 2019 the 4th Report ex-Art. 17 on the conservation status (CS) of Annex I Habitats of the 92/43/EEC Directive was expected by every EU/28 country, with reference to the period 2013-18. In Italy, the process was in charge to the Italian Institute for Environmental Protection and Research (ISPRA), on behalf of the Ministry for Environment, Land and Sea Protection (MATTM), with the scientific support of the Italian Botanical Society (SBI). A large group of thematic and territorial experts elaborated the available data concerning the 124 types of terrestrial and inland water Habitats present in Italy, 39 of which are represented by Forest Habitats (Group 9),. The main aim of the work was the evaluation of the overall CS of each Habitat by Biogeographic Region (Mediterranean, Continental and Alpine), for a total amount of 294 assessments. A high proportion of these (92, corresponding to 31% of the total) referred to Forest Habitats, including 20 marginal types for which the CS was not requested. The analysis was carried out at different scales: a) administrative territory, through the data contained in the ISPRA database, whose compilation was in charge to the Regions and Autonomous Provinces; b) Natura 2000 site, with the latest updates available (Standard Data Forms updated to 2018); c) national scale, implementing the distribution maps for each Habitat based on the European grid ETRS89-LAEA5210 (10x10 km2 mesh); d) Biogeographic Region, scale of the final assessment. Cartographic outcomes, associated databases and additional data used for the assessments will be available online on the ISPRA Portal as soon as the validation process by the European Commission will be completed. A dedicated archive named "HAB_IT" has been created in the national database "VegItaly" (1), managed by the Italian Society of Vegetation Science, where the phytosociological relevés representative of the various Annex I Habitats in Italy will be archived and freely accessible. An overview of the results regarding the Forest habitats is here provided, including a comparison with the outcomes of the former reporting cycle, the 3rd Report ex-Art. 17 (2). In several cases (e.g. 9120, 91L0), the distribution maps have been remarkably improved due to better knowledge and more fitful interpretation. The conservation status resulted as Favourable (FV) for 6,7%, Inadequate (U1) for 58,7% and Bad (U1) for 32,0% of the 72 assessed forest Habitat types. In no case there was an improvement of the conservation status, while in 6 cases a worsening of the conditions resulted from the data analysis, pointing out the Habitats types with a higher need of action. Similarly to other projects carried out as a team by the network of Annex I Habitat experts of the Italian Botanical Society and the Italian Society for Vegetation Science (e.g. 3, 4), this is another step in the direction of supporting the implementation of the 92/43/EEC "Habitat" Directive in Italy and Europe. On this ground, the high biodiversity of the Italian forest Habitats could be emphasized, however results pointed out that some rare or endemic types (e.g. Alnus cordata or Betula aetnensis-dominated forests) are still scarcely acknowledged by the most prominent EU conservation tools such as the Annex I to the "Habitat" Directive. 1) F. Landucci et al. (2012) Plant Biosyst., 146(4), 756-763 2) P. Genovesi et al. (2014) ISPRA, Serie Rapporti, 194/2014 3) E. Biondi et al. (2009) Società Botanica Italiana, MATTM, D.P.N., http://vnr.unipg.it/habitat/ 4) D. Gigante et al. (2016) Plant Sociology, 53(2), 77-8

Shedding light on typical species : implications for habitat monitoring

Habitat monitoring in Europe is regulated by Article 17 of the Habitats Directive, which suggests the use of typical species to assess habitat conservation status. Yet, the Directive uses the term “typical” species but does not provide a definition, either for its use in reporting or for its use in impact assessments. To address the issue, an online workshop was organized by the Italian Society for Vegetation Science (SISV) to shed light on the diversity of perspectives regarding the different concepts of typical species, and to discuss the possible implications for habitat monitoring. To this aim, we inquired 73 people with a very different degree of expertise in the field of vegetation science by means of a tailored survey composed of six questions. We analysed the data using Pearson's Chi-squared test to verify that the answers diverged from a random distribution and checked the effect of the degree of experience of the surveyees on the results. We found that most of the surveyees agreed on the use of the phytosociological method for habitat monitoring and of the diagnostic and characteristic species to evaluate the structural and functional conservation status of habitats. With this contribution, we shed light on the meaning of “typical” species in the context of habitat monitoring