A global Nullstellensatz for ideals of Denjoy-Carleman functions

We prove a Nullstellensatz result for global ideals of Denjoy-Carleman functions in both finitely generated and infinitely generated cases.Comment: 5 page

On globally defined semianalytic sets

In this work we present the concept of $C$-semianalytic subset of a real analytic manifold and more generally of a real analytic space. $C$-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan ($C$-analytic sets for short). More precisely $S$ is a $C$-semianalytic subset of a real analytic space $(X,{\mathcal O}_X)$ if each point of $X$ has a neighborhood $U$ such that $S\cap U$ is a finite boolean combinations of global analytic equalities and strict inequalities on $X$. By means of paracompactness $C$-semianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on $X$. The family of $C$-semianalytic sets is closed under the same operations as the family of semianalytic sets: locally finite unions and intersections, complement, closure, interior, connected components, inverse images under analytic maps, sets of points of dimension $k$, etc. although they are defined involving only global analytic functions. In addition, we characterize subanalytic sets as the images under proper analytic maps of $C$-semianalytic sets. We prove also that the image of a $C$-semianalytic set $S$ under a proper holomorphic map between Stein spaces is again a $C$-semianalytic set. The previous result allows us to understand better the structure of the set $N(X)$ of points of non-coherence of a $C$-analytic subset $X$ of a real analytic manifold $M$. We provide a global geometric-topological description of $N(X)$ inspired by the corresponding local one for analytic sets due to Tancredi-Tognoli (1980), which requires complex analytic normalization. As a consequence it holds that $N(X)$ is a $C$-semianalytic set of dimension $\leq\dim(X)-2$.Comment: 32 pages, 3 figure

Influence of pH on the kinetics of hydrolysis reactions: the case of epichlorohydrin and glycidol

Glycidol (GL) and epichlorohydrin (EPI) are two widely used molecules in chemical, pharmaceutical and food industry applications. However, their use in aqueous environments causes the formation of compounds, like monochloropropanediol (MCPD) and dichloropropanol (DCP), reported as dangerous for human health and therefore regulated by severe law restrictions. To identify the conditions leading to such species and design the corresponding processes in order to prevent their formation, hydrolysis and chlorination of EPI and GL, together with dehydrohalogenation of DCP and MCPD, have been systematically analysed. Different reaction conditions in terms of temperature, pH and chloride ion concentration have been experimentally investigated and the concentration of the involved species was tracked over time by gas chromatography and high-performance liquid chromatography. These experimental data were fitted through a kinetic model, which allowed a general expression of the observed rate constant of each reaction as a function of temperature and pH to be quantified. In particular, the reaction rates are conveniently expressed as combinations of three contributions: alkaline, neutral and acid. The corresponding rate laws explicitly account for the critical role of pH. The developed mechanistic model exhibits good prediction ability and may represent the basis for optimising processes employing EPI and GL

On the Hilbert 17th problem for global analytic functions

We consider Hilbert’s 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the solution of the problem and the computation of Pythagoras numbers of meromorphic function

Assessment of listing and categorisation of animal diseases within the framework of the Animal Health Law (Regulation (EU) No 2016/429): antimicrobial-resistant Rhodococcus equi in horses

Rhodococcus equi (R. equi) was identified among the most relevant antimicrobial-resistant (AMR) bacteria in the EU for horses in a previous scientific opinion. Thus, it has been assessed according to the criteria of the Animal Health Law (AHL), in particular criteria of Article 7 on disease profile and impacts, Article 5 on its eligibility to be listed, Annex IV for its categorisation according to disease prevention and control rules as in Article 9 and Article 8 for listing animal species related to the bacterium. The assessment has been performed following a methodology previously published. The outcome is the median of the probability ranges provided by the experts, which indicates whether each criterion is fulfilled (lower bound ≥ 66%) or not (upper bound ≤ 33%), or whether there is uncertainty about fulfilment. Reasoning points are reported for criteria with uncertain outcome. According to the assessment here performed, it is uncertain whether AMR R. equi can be considered eligible to be listed for Union intervention according to Article 5 of the AHL (10–66% probability). According to the criteria in Annex IV, for the purpose of categorisation related to the level of prevention and control as in Article 9 of the AHL, the AHAW Panel concluded that the bacterium does not meet the criteria in Sections 1 and 2 (Categories A and B; 5–10% and 10–33% probability of meeting the criteria, respectively), and the AHAW Panel is uncertain whether it meets the criteria in Sections 3, 4 and 5 (Categories C, D and E; 10–66% probability of meeting the criteria in all three categories). The animal species to be listed for AMR R. equi according to Article 8 criteria are mainly horses and other species belonging to the Perissodactyla and Artiodactyla orders.info:eu-repo/semantics/publishedVersio

Assessment of listing and categorisation of animal diseases within the framework of the Animal Health Law (Regulation (EU) No 2016/429): antimicrobial-resistant Staphylococcus pseudintermedius in dogs and cats

Staphylococcus pseudintermedius (S. pseudintermedius) was identified among the most relevant antimicrobial-resistant (AMR) bacteria in the EU for dogs and cats in a previous scientific opinion. Thus, it has been assessed according to the criteria of the Animal Health Law (AHL), in particular criteria of Article 7 on disease profile and impacts, Article 5 on its eligibility to be listed, Annex IV for its categorisation according to disease prevention and control rules as in Article 9, and Article 8 for listing animal species related to the bacterium. The assessment has been performed following a methodology previously published. The outcome is the median of the probability ranges provided by the experts, which indicates whether each criterion is fulfilled (lower bound ≥ 66%) or not (upper bound ≤ 33%), or whether there is uncertainty about fulfilment. Reasoning points are reported for criteria with uncertain outcome. According to the assessment here performed, it is uncertain whether AMR S. pseudintermedius can be considered eligible to be listed for Union intervention according to Article 5 of the AHL (30–90% probability). According to the criteria in Annex IV, for the purpose of categorisation related to the level of prevention and control as in Article 9 of the AHL, the AHAW Panel concluded that the bacterium does not meet the criteria in Sections 1, 2 and 4 (Categories A, B and D; 0–1%, 1–10% and 10–33% probability of meeting the criteria, respectively) and the AHAW Panel is uncertain whether it meets the criteria in Sections 3 and 5 (Categories C and E, 5–66% and 30–90% probability of meeting the criteria, respectively). The animal species to be listed for AMR S. pseudintermedius according to Article 8 criteria are mostly species belonging to the families of Canidae and Felidae, such as dogs and cats.info:eu-repo/semantics/publishedVersio