The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(\lambda)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$_S= +\lambda <{{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}>,$$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $\lambda$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez lagomasino on the occasion of his 60th birthday, accepted in Journal of Approximation Theor

Community, work and family in diverse contexts and changing times

The 8th International Community, Work and Family conference took place in Malta at the Valletta campus of the University of Malta between the 23rd to the 25th May 2019. In a pre-COVID-19 world with no traveling restrictions, the conference brought together over 100 experts, academics, and students from a broad range of countries and disciplines to focus on the theme of Community, Work and Family in Diverse Contexts and Changing Times. The research presented during the conference highlights some of the challenges that communities, organizations and families are facing in the twenty-first century across diverse and rapidly changing contexts. The topics presented spanned from broad studies that analyze the work-life interface of well-studied groups such as fathers and mothers, to other clusters that are generally less well-researched such as the police and the military, migrants, solo entrepreneurs, the LGBTIQ community, and those who work with people with special needs. The recurrent theme of the gendered division of labor and work-life measures was discussed by various researchers, as were the issues of flexible work, family policy, and the impact of technology. It was refreshing to note that various researchers focused on the issue of community as a source of support, whilst others explored how peer, supervisor and management support impacts work-life issues. Overall, the conference provided a diverse and rich range of scholarly material upon which to develop this special issue for Community, Work & Family. [...

The sigma invariants for the golden mean Thompson group

We use a method of Bieri, Geoghegan and Kochloukova to calculate the BNSR-invariants for the Golden-Mean Thompson’s group. To do so we establish conditions under which the Sigma invariants coincide with those of a subgroup of finite index, addressing a problem posed by Strebel

The Sigma invariants for the Golden Mean Thompson group

We use a method of Bieri, Geoghegan and Kochloukova to calculate the BNSR-invariants for the irrational slope Thompson's group $F_{\tau}$. To do so we establish conditions under which the Sigma invariants coincide with those of a subgroup of finite index, addressing a problem posed by Strebel.Comment: 19 pages. v2: Major revision after referee's comments, corrected inacurracies/inconsistencies throughout the text, improved proof of the main theorem, restated results on Sigma invariants and characters for clarity, expanded on related work. Final version, to appear in the New York Journal of Mathematic

The Gromov Norm of the Product of Two Surfaces

We make an estimation of the value of the Gromov norm of the Cartesian product of two surfaces. Our method uses a connection between these norms and the minimal size of triangulations of the products of two polygons. This allows us to prove that the Gromov norm of this product is between 32 and 52 when both factors have genus 2. The case of arbitrary genera is easy to deduce form this one.Comment: The journal version contains an error that invalidates one direction of the main theorem. The present version contains an erratum, at the end, explaining thi

Medical Simulation Training on Trauma-Informed Care in the Emergency Department

Learning Objectives: To describe a novel simulation training developed to teach Trauma-Informed Care principles and applications for patient care in Emergency Medicine. To present results from pre- and post-surveys about effectiveness of simulations to learn and apply Trauma-Informed Care in acute-care settings.Introduction/Background: Emergency Medicine physicians often care for patients experiencing direct sequelae from traumatic events including abuse, discrimination, and violence. Trauma-Informed Care (TIC) is a framework that recognizes the prevalence of trauma, promotes patient empowerment, and aims to minimize retraumatization. Limited curriculum on TIC in acute-care settings exists despite its widespread utility, with medical simulations (SIM) presenting a novel educational opportunity for this aim.Educational Objectives: Describe principles of TIC and its importance in clinical practice. Present strategies for performing TIC-guided history taking and physical exams. Discuss situations when trauma screenings are indicated for patient safety and care. Facilitate the practice of TIC in acute-care settings.Curricular Design: An SIM workshop reproducing relevant clinical encounters was developed for medical students to practice implementing TIC in the Emergency Department (ED). Students attended a didactic on TIC fundamentals and its applications in clinical care. Small groups then interacted with three SIM cases caring for patients with urgent medical needs and pertinent history related to intimate partner violence, transgender health, and discrimination in the healthcare system.Impact/Effectiveness: Application of TIC principles is essential to providing patient-centered care in the ED. A pilot group of 12 students participated in these SIM sessions. The workshop was well-received, as 100% of participants found simulation training “Very” or “Extremely Useful” in preparing to apply TIC in patient interactions, compared to 42% prior to the session (p&lt;0.05). Students also developed relevant skills, as 42% of students felt “Very” or “Extremely Confident” in using appropriate TIC language during physical exams, compared to 0% initially (p&lt;0.05). Overall, this novel intervention represents a feasible and effective session for teaching TIC skills in Emergency Medicine

Correlations between 21 cm Radiation and the CMB from Active Sources

Neutral hydrogen is ubiquitous, absorbing and emitting 21 cm radiation throughout much of the Universe's history. Active sources of perturbations, such as cosmic strings, would generate simultaneous perturbations in the distribution of neutral hydrogen and in the Cosmic Microwave Background (CMB) radiation from recombination. Moving strings would create wakes leading to 21 cm brightness fluctuations, while also perturbing CMB light via the Gott-Kaiser-Stebbins effect. This would lead to spatial correlations between the 21 cm and CMB anisotropies. Passive sources, like inflationary perturbations, predict no cross correlations prior to the onset of reionization. Thus, observation of any cross correlation between CMB and 21 cm radiation from dark ages would constitute evidence for new physics. We calculate the cosmic string induced correlations between CMB and 21 cm and evaluate their observability.Comment: 8 pages, 5 figure

Probing the first galaxies with the SKA

Observations of anisotropies in the brightness temperature of the 21 cm line of neutral hydrogen from the period before reionization would shed light on the dawn of the first stars and galaxies. In this paper, we use large-scale semi-numerical simulations to analyse the imprint on the 21 cm signal of spatial fluctuations in the Lyman-alpha flux arising from the clustering of the first galaxies. We show that an experiment such as the Square Kilometer Array (SKA) can probe this signal at the onset of reionization, giving us important information about the UV emission spectra of the first stars and characterizing their host galaxies. SKA-pathfinders with ~ 10% of the full collecting area should be capable of making a statistical detection of the 21 cm power spectrum at redshifts z 67 MHz). We then show that the SKA should be able to measure the three dimensional power spectrum as a function of the angle with the line of sight and discuss the use of the redshift space distortions as a way to separate out the different components of the 21 cm power spectrum. We demonstrate that, at least on large scales where the Lyman-alpha fluctuations are linear, they can be used as a model independent way to extract the power spectra due to these Lyman-alpha fluctuations.Comment: 13 pages, 17 figures. New version to match version accepted by A&A. Improved discussions on the Lyman-alpha simulation, adiabatic cooling fluctuations, the Fisher matrix approach and the Poisson term calculation. New version of the code available at: http://www.SimFast21.or

Development of a Tool to Recreate the Mars Science Laboratory Aerothermal Environment

The Mars Science Laboratory will enter the Martian atmosphere in 2012 with multiple char depth sensors and in-depth thermocouples in its heatshield. The aerothermal environment experienced by MSL may be computationally recreated using the data from the sensors and a material response program, such as the Fully Implicit Ablation and Thermal (FIAT) response program, through the matching of the char depth and thermocouple predictions of the material response program to the sensor data. A tool, CHanging Inputs from the Environment of FIAT (CHIEF), was developed to iteratively change different environmental conditions such that FIAT predictions match within certain criteria applied to an external data set. The computational environment is changed by iterating on the enthalpy, pressure, or heat transfer coefficient at certain times in the trajectory. CHIEF was initially compared against arc-jet test data from the development of the MSL heatshield and then against simulated sensor data derived from design trajectories for MSL. CHIEF was able to match char depth and in-depth thermocouple temperatures within the bounds placed upon it for these cases. Further refinement of CHIEF to compare multiple time points and assign convergence criteria may improve accuracy