Global Existence Results and Uniqueness for Dislocation Equations

We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and non monotone case

Philosophy and Science in Leibniz

This paper explores the question of Leibniz’s contribution to the rise of modern ‘science’. To be sure, it is now generally agreed that the modern category of ‘science’ did not exist in the early modern period. At the same time, this period witnessed a very important stage in the process from which modern science eventually emerged. My discussion will be aimed at uncovering the new enterprise, and the new distinctions which were taking shape in the early modern period under the banner of the old Aristotelian terminology. I will argue that Leibniz begins to theorize a distinction between physics and metaphysics that tracks our distinction between the autonomous enterprise of science in its modern meaning, and the enterprise of philosophy. I will try to show that, for Leibniz, physics proper is the study of natural phenomena in mathematical and mechanical terms without recourse for its explanations to metaphysical notions. This autonomy, however, does not imply for Leibniz that physics can say on its own all that there is to be said about the natural world. Quite the opposite. Leibniz inherits from the Aristotelian tradition the view that physics needs metaphysical roots or a metaphysical grounding. For Leibniz, what is ultimately real is reached by metaphysics, not by physics. This is, in my view, Leibniz’s chief insight: the new mathematical physics is an autonomous enterprise which offers its own kind of explanations but does not exhaust what can (and should) be said about the natural world

The N-Terminal, Polybasic Region Is Critical for Prion Protein Neuroprotective Activity

Several lines of evidence suggest that the normal form of the prion protein, PrPC, exerts a neuroprotective activity against cellular stress or toxicity. One of the clearest examples of such activity is the ability of wild-type PrPC to suppress the spontaneous neurodegenerative phenotype of transgenic mice expressing a deleted form of PrP (Δ32–134, called F35). To define domains of PrP involved in its neuroprotective activity, we have analyzed the ability of several deletion mutants of PrP (Δ23–31, Δ23–111, and Δ23–134) to rescue the phenotype of Tg(F35) mice. Surprisingly, all of these mutants displayed greatly diminished rescue activity, although Δ23–31 PrP partially suppressed neuronal loss when expressed at very high levels. Our results pinpoint the N-terminal, polybasic domain as a critical determinant of PrPC neuroprotective activity, and suggest that identification of molecules interacting with this region will provide important clues regarding the normal function of the protein. Small molecule ligands targeting this region may also represent useful therapeutic agents for treatment of prion diseases

Global disparities in surgeons’ workloads, academic engagement and rest periods: the on-calL shIft fOr geNEral SurgeonS (LIONESS) study

: The workload of general surgeons is multifaceted, encompassing not only surgical procedures but also a myriad of other responsibilities. From April to May 2023, we conducted a CHERRIES-compliant internet-based survey analyzing clinical practice, academic engagement, and post-on-call rest. The questionnaire featured six sections with 35 questions. Statistical analysis used Chi-square tests, ANOVA, and logistic regression (SPSS® v. 28). The survey received a total of 1.046 responses (65.4%). Over 78.0% of responders came from Europe, 65.1% came from a general surgery unit; 92.8% of European and 87.5% of North American respondents were involved in research, compared to 71.7% in Africa. Europe led in publishing research studies (6.6 ± 8.6 yearly). Teaching involvement was high in North America (100%) and Africa (91.7%). Surgeons reported an average of 6.7 ± 4.9 on-call shifts per month, with European and North American surgeons experiencing 6.5 ± 4.9 and 7.8 ± 4.1 on-calls monthly, respectively. African surgeons had the highest on-call frequency (8.7 ± 6.1). Post-on-call, only 35.1% of respondents received a day off. Europeans were most likely (40%) to have a day off, while African surgeons were least likely (6.7%). On the adjusted multivariable analysis HDI (Human Development Index) (aOR 1.993) hospital capacity > 400 beds (aOR 2.423), working in a specialty surgery unit (aOR 2.087), and making the on-call in-house (aOR 5.446), significantly predicted the likelihood of having a day off after an on-call shift. Our study revealed critical insights into the disparities in workload, access to research, and professional opportunities for surgeons across different continents, underscored by the HDI

Realismo, pragmatismo, naturalismo. Le trasformazioni della fenomenologia in Nord America

The purpose of this issue of “Discipline filosofiche” is to assess the process of re-elaboration and re-definition that Husserl’s phenomenology underwent in North America not only from the standpoint of its historical-philosophical implications, but especially in view of its theoretical outcomes. The underlying conviction is that an “intensional” approach to that history can yield a new interpretative canon for Husserlian phenomenology. However, a limit of this approach is that it overlooks the problem of the assimilation of this European tradition within the North American context. Therefore, in this issue we have relaxed, to use Quine’s words, the demand for definition, and have explored in a more pragmatic fashion the different ways in which the word “phenomenology” has been translated and employed in the North American philosophical context

Regularity theorems in limit cases for solutions of linear and nonlinear elliptic equations

In questo lavoro otteniamo risultati di regolarità per le soluzioni di equazioni ellittiche lineari e fortemente non lineari con termini di ordine inferiore Lu = -(fi)x$_{i}$ in un sottoinsieme aperto limitato $\Omega$ di R$^{n}$. Dimostriamo che u appartiene allo spazio di Orlicz L$_{\textrm{Ø}}(\Omega)(\textrm{Ø(t)=exp}\mid t\mid^{n/(n-1)}-1$) quando fi $\epsilon\textrm{L}^{n/(p-1)}(\Omega),$ i=1,2,...,n, dove p=1 nel caso lineare.In this paper we obtain regularity results for the solutions u of linear ad strongly nonlinear elliptic equations with lower order terms Lu = -(fi)x$_{i}$ in a bouded open subset $\Omega$ of R$^{n}$. We prove that u belongs to the Orlicz space L$_{\textrm{Ø}}(\Omega)(\textrm{Ø(t)=exp}\mid t\mid^{n/(n-1)}-1$) when fi $\epsilon\textrm{L}^{n/(p-1)}(\Omega),$ i=1,2,...,n, where p=1 in the linear case

Geotechnical engineering practice and the implementation of Eurocode approach in Italy

Since 2003 several efforts have been done in Italy by the Italian Government to modify Technical Standards, abandoning the conventional allowable stress approach and introducing the limit state approach, according to Eurocodes. More specifically in the paper the following aspects are discussed: a) the intrinsic incompatibility between the Eurocode approach and the Italian Legislation as far as the responsibilities of practising engineers are concerned; b) resistance of practising engineers and geologists to abandon conventional design methods together with a generalized reluctance in Italy towards continuous education programs; c) intrinsic incompatibility between EC7 (2004) and "structural" Eurocodes (more specifically EC8 (2004)). Eventually the difficulties of introducing the limit state approach in conventional education programs are discussed. © 2008 Taylor & Francis Group, London