Boundary behavior of analytic functions of two variables via generalized models

We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the 2-torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two function-theoretic problems. The first of these is to characterise the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carath\'eodory condition holds. The second is to obtain a representation theorem for functions in the two-variable Pick class analogous to the refined Nevanlinna representation of functions in the one-variable Pick class.Comment: 30 page

Nevanlinna representations in several variables

We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.Comment: 37 pages. In this version we have added some references and expanded the introductio

CV20016

This report provides the main results and findings of the nineteenth annual underwater television survey on the Aran, Galway Bay and Slyne head Nephrops grounds, ICES assessment area; Functional Unit 17. The survey was multi-disciplinary in nature collecting UWTV, CTD and other ecosystem data. In 2020 a total of 44 UWTV stations were successfully completed, 34 on the Aran Grounds, 5 on Galway Bay and 5 on Slyne Head patches. The mean burrow density observed in 2020, adjusted for edge effect, was medium at 0.29 burrows/m². The final krigged burrow abundance estimate for the Aran Grounds was 359 million burrows with a CV (Coefficient of Variance; relative standard error) of 4%. The final abundance estimate for Galway Bay was 27 million and for Slyne Head was 7 million, with CVs of 13% and 4% respectively. The total abundance estimates have fluctuated considerably over the time series. The 2020 combined abundance estimate (394 million burrows) is 20% lower than in 2019, and it is below the MSY Btrigger reference point (540 million burrows). Using the 2020 estimate of abundance and updated stock data implies catches between 443 and 508 tonnes in 2021 that correspond to the F ranges in the EU multi annual plan for Western Waters, assuming that discard rates and fishery selection patterns do not change from the average of 2017–2019. Virgularia mirabilis was the only sea-pen species observed on the UWTV footage. Trawl marks were present at 7% of the Aran stations surveyed

CV20019

This report provides the main results of the eleventh underwater television survey of the various Nephrops patches in Functional Unit 19. The survey was multi-disciplinary in nature collecting UWTV, multi-beam and other ecosystem data. In 2020 a total 42 UWTV stations were successfully completed. The mean density estimates varied considerably across the different patches. The 2020 raised abundance estimate was a 20% decrease from the 2019 estimate and at 320 million burrows is below the MSY Btrigger reference point (430 million). Using the 2020 estimate of abundance and updated stock data implies catch in 2021 that correspond to the F ranges in the EU multi annual plan for Western Waters are between 531 and 595 tonnes (assuming that discard rates and fishery selection patterns do not change from the average of 2017–2019). Two species of sea pen were observed; Virgularia mirabilis and Pennatula phosphorea which have been observed on previous surveys of FU19. Trawl marks were observed at 26% of the stations surveyed

The Survey for Ionization in Neutral Gas Galaxies- II. The Star Formation Rate Density of the Local Universe

We derive observed Halpha and R band luminosity densities of an HI-selected sample of nearby galaxies using the SINGG sample to be l_Halpha' = (9.4 +/- 1.8)e38 h_70 erg s^-1 Mpc^-3 for Halpha and l_R' = (4.4 +/- 0.7)e37 h_70 erg s^-1 A^-1 Mpc^-3 in the R band. This R band luminosity density is approximately 70% of that found by the Sloan Digital Sky Survey. This leads to a local star formation rate density of log(SFRD) = -1.80 +0.13/-0.07(random) +/- 0.03(systematic) + log(h_70) after applying a mean internal extinction correction of 0.82 magnitudes. The gas cycling time of this sample is found to be t_gas = 7.5 +1.3/-2.1 Gyr, and the volume-averaged equivalent width of the SINGG galaxies is EW(Halpha) = 28.8 +7.2/-4.7 A (21.2 +4.2/-3.5 A without internal dust correction). As with similar surveys, these results imply that SFRD(z) decreases drastically from z ~ 1.5 to the present. A comparison of the dynamical masses of the SINGG galaxies evaluated at their optical limits with their stellar and HI masses shows significant evidence of downsizing: the most massive galaxies have a larger fraction of their mass locked up in stars compared with HI, while the opposite is true for less massive galaxies. We show that the application of the Kennicutt star formation law to a galaxy having the median orbital time at the optical limit of this sample results in a star formation rate decay with cosmic time similar to that given by the SFRD(z) evolution. This implies that the SFRD(z) evolution is primarily due to the secular evolution of galaxies, rather than interactions or mergers. This is consistent with the morphologies predominantly seen in the SINGG sample.Comment: 15 pages, 5 figures, ApJ in press. Data available at http://sungg.pha.jhu.edu/PubData/ Corrected: Minor typos and formatting issues fixe

Enhancing father engagement in parenting programs: Translating research into practice recommendations

Objective Given the increasing research and practice interest in father engagement, this article aimed to develop a clinical narrative integrating the extant research literature to distil key practice recommendations for enhancing father engagement in parenting interventions for child wellbeing. Method A narrative review of research on father engagement in interventions for child wellbeing was conducted, to identify and distil evidence‐based policies and practices to enhance father engagement for practitioners and organisations. Results Six broad policy and practice recommendations are provided that pertain to: engaging the parenting team, avoiding a father deficit model, increasing father awareness of parenting interventions, ensuring father‐inclusive program content and delivery, increasing organisational support for father‐inclusive practice, and increasing professional father engagement training. Conclusion This review provides practitioners with guidelines for enhancing father engagement based on the available research. It also provides recommendations for further research regarding the effectiveness of strategies to enhance father engagement

Large-scale collective motion of RFGC galaxies

We processed the data about radial velocities and HI linewidths for 1678 flat edge-on spirals from the Revised Flat Galaxy Catalogue. We obtained the parameters of the multipole components of large-scale velocity field of collective non-Hubble galaxy motion as well as the parameters of the generalized Tully-Fisher relationship in the "HI line width - linear diameter" version. All the calculations were performed independently in the framework of three models, where the multipole decomposition of the galaxy velocity field was limited to a dipole, quadrupole and octopole terms respectively. We showed that both the quadrupole and the octopole components are statistically significant. On the basis of the compiled list of peculiar velocities of 1623 galaxies we obtained the estimations of cosmological parameters Omega_m and sigma_8. This estimation is obtained in both graphical form and as a constraint of the value S_8=sigma_8(Omega_m/0.3)^0.35 = 0.91 +/- 0.05.Comment: Accepted for publication in Astrophysics and Space Scienc

Nevanlinna representations in several variables

We generalize to several variables the classical theorem of Nevanlinna that characterizes the Cauchy transforms of positive measures on the real line. We show that for the Loewner class, a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane, there are representation formulae in terms of densely-defined self-adjoint operators on a Hilbert space. We identify four types of such representations, and we obtain function-theoretic conditions that are necessary and sufficient for a given function to possess a representation of each of the four types

Russia’s idea of the multipolar world order: origins and main dimensions

Contemporary international relations are rife with the ideological struggle over the potential nature of the rapidly changing world order. Two distinct paradigmatic positions have surfaced. One champions economic, cultural, and political globalization conducted under the leadership of the Western world. The other advocates a more particularistic approach that fends for a balance of interests, multiplicity of politico-cultural forms and multiple centers of international influence. The latter doctrine, often referred to as the multipolar world theory, is the subject of this paper. The discussion argues that the idea of a multipolar world order has emerged as Russia’s main ethical and ideological position advanced in the international arena. Its philosophical tenets buttress Russian society intellectually at home, providing the expedients to pursue the country’s foreign policy goals abroad. The paper examines a substantial value package with roots in both Russian and Western philosophy that sustains the multipolar world order theory