Two-point boundary value problems for linear evolution equations

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L, 0 < t < T, with L and T positive nite constants. We present a general method for identifying well-posed problems, as well as for constructing an explicit representation of the solution of such problems. This representation has explicit x and t dependence, and it consists of an integral in the k-complex plane and of a discrete sum. As illustrative examples we solve some two-point boundary value problems for the equations iqt + qxx = 0 and qt + qxxx = 0

The Unified Method: I Non-Linearizable Problems on the Half-Line

Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex $k$-plane (the Fourier plane), which has a jump matrix with explicit $(x,t)$-dependence involving four scalar functions of $k$, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved simply using algebraic manipulations. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant, and on the computation of the large $k$ asymptotics of the eigenfunctions defining the relevant spectral functions.Comment: 39 page

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C =∇× B, is rationalized via a second-rank anapole magnetizability tensor aαβ , defined as minus the second derivative of the second-order interaction energy with respect to the components Cα and Bβ. The average anapole magnetizability a equals −χ, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χα,βγ . It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole Aα, having the same magnitude, but opposite sign, for two enantiomorphs.Fil: Pagola, Gabriel Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Ferraro, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Provasi, Patricio Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnologica; ArgentinaFil: Pelloni, Stefano. Universidad de Modena y Reggio Emilia. Departamento de Química; ItaliaFil: Lazzeretti, Paolo. Universidad de Modena y Reggio Emilia. Departamento de Química; Italia; Itali

The joint evaluated fission and fusion nuclear data library, JEFF-3.3

The joint evaluated fission and fusion nuclear data library 3.3 is described. New evaluations for neutron-induced interactions with the major actinides $^{235}$U, $^{238}$U and $^{239}$Pu, on $^{241}$Am and $^{23}$Na, $^{59}$Ni, Cr, Cu, Zr, Cd, Hf, W, Au, Pb and Bi are presented. It includes new fission yields, prompt fission neutron spectra and average number of neutrons per fission. In addition, new data for radioactive decay, thermal neutron scattering, gamma-ray emission, neutron activation, delayed neutrons and displacement damage are presented. JEFF-3.3 was complemented by files from the TENDL project. The libraries for photon, proton, deuteron, triton, helion and alpha-particle induced reactions are from TENDL-2017. The demands for uncertainty quantification in modeling led to many new covariance data for the evaluations. A comparison between results from model calculations using the JEFF-3.3 library and those from benchmark experiments for criticality, delayed neutron yields, shielding and decay heat, reveals that JEFF-3.3 performes very well for a wide range of nuclear technology applications, in particular nuclear energy

Diversity and ethics in trauma and acute care surgery teams: results from an international survey

Background: Investigating the context of trauma and acute care surgery, the article aims at understanding the factors that can enhance some ethical aspects, namely the importance of patient consent, the perceptiveness of the ethical role of the trauma leader, and the perceived importance of ethics as an educational subject. Methods: The article employs an international questionnaire promoted by the World Society of Emergency Surgery. Results: Through the analysis of 402 fully filled questionnaires by surgeons from 72 different countries, the three main ethical topics are investigated through the lens of gender, membership of an academic or non-academic institution, an official trauma team, and a diverse group. In general terms, results highlight greater attention paid by surgeons belonging to academic institutions, official trauma teams, and diverse groups. Conclusions: Our results underline that some organizational factors (e.g., the fact that the team belongs to a university context or is more diverse) might lead to the development of a higher sensibility on ethical matters. Embracing cultural diversity forces trauma teams to deal with different mindsets. Organizations should, therefore, consider those elements in defining their organizational procedures. Level of evidence: Trauma and acute care teams work under tremendous pressure and complex circumstances, with their members needing to make ethical decisions quickly. The international survey allowed to shed light on how team assembly decisions might represent an opportunity to coordinate team member actions and increase performance

Team dynamics in emergency surgery teams: results from a first international survey

Background: Emergency surgery represents a unique context. Trauma teams are often multidisciplinary and need to operate under extreme stress and time constraints, sometimes with no awareness of the trauma\u2019s causes or the patient\u2019s personal and clinical information. In this perspective, the dynamics of how trauma teams function is fundamental to ensuring the best performance and outcomes. Methods: An online survey was conducted among the World Society of Emergency Surgery members in early 2021. 402 fully filled questionnaires on the topics of knowledge translation dynamics and tools, non-technical skills, and difficulties in teamwork were collected. Data were analyzed using the software R, and reported following the Checklist for Reporting Results of Internet E-Surveys (CHERRIES). Results: Findings highlight how several surgeons are still unsure about the meaning and potential of knowledge translation and its mechanisms. Tools like training, clinical guidelines, and non-technical skills are recognized and used in clinical practice. Others, like patients\u2019 and stakeholders\u2019 engagement, are hardly implemented, despite their increasing importance in the modern healthcare scenario. Several difficulties in working as a team are described, including the lack of time, communication, training, trust, and ego. Discussion: Scientific societies should take the lead in offering training and support about the abovementioned topics. Dedicated educational initiatives, practical cases and experiences, workshops and symposia may allow mitigating the difficulties highlighted by the survey\u2019s participants, boosting the performance of emergency teams. Additional investigation of the survey results and its characteristics may lead to more further specific suggestions and potential solutions

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

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework