A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.Comment: 30 pages; corrected typos and fixed incomplete proofs in section

Growing massive black holes through super-critical accretion of stellar-mass seeds

The rapid assembly of the massive black holes that power the luminous quasars observed at $z \sim 6-7$ remains a puzzle. Various direct collapse models have been proposed to head-start black hole growth from initial seeds with masses $\sim 10^5\,\rm M_\odot$, which can then reach a billion solar mass while accreting at the Eddington limit. Here we propose an alternative scenario based on radiatively inefficient super-critical accretion of stellar-mass holes embedded in the gaseous circum-nuclear discs (CNDs) expected to exist in the cores of high redshift galaxies. Our sub-pc resolution hydrodynamical simulations show that stellar-mass holes orbiting within the central 100 pc of the CND bind to very high density gas clumps that arise from the fragmentation of the surrounding gas. Owing to the large reservoir of dense cold gas available, a stellar-mass black hole allowed to grow at super-Eddington rates according to the "slim disc" solution can increase its mass by 3 orders of magnitudes within a few million years. These findings are supported by simulations run with two different hydro codes, RAMSES based on the Adaptive Mesh Refinement technique and GIZMO based on a new Lagrangian Godunov-type method, and with similar, but not identical, sub-grid recipes for star formation, supernova feedback, black hole accretion and feedback. The low radiative efficiency of super-critical accretion flows are instrumental to the rapid mass growth of our black holes, as they imply modest radiative heating of the surrounding nuclear environment.Comment: 12 pages, 8 figures, 2 tables. Accepted for publication in MNRA

The Emotional Self-Efficacy Scale: Adaptation and Validation for Young Adolescents

Emotional self-efficacy (ESE) is an important aspect of emotional functioning, with current measures for children and adolescents focused on the measurement of self-beliefs in relation to the management of emotions. In the present study, we report the psychometric properties of the first adaptation of the Emotional Self-Efficacy Scale for youth (Youth-ESES) that measures additional aspects of ESE, such as perceiving and understanding emotions and helping others modulate their emotions. Participants were 192 young adolescents aged 11 to 13 years from a U.K. state school. They completed the Youth-ESES and measures of ability emotional intelligence (EI) and cognitive ability. Results support the same four-factor structure that has been previously documented using the adult version of the ESES, with the four subscales being largely independent from cognitive ability and only moderately related to ability EI. However, the four subscales were less differentiated in the present study compared with adult data previously published, suggesting that there is a strong general factor underlying young adolescents’ ESE scores. Overall, the results suggest that the adapted Youth-ESES can be reliably used with youth, and that confidence in how a young person feels about his or her emotional functioning remains distinct from emotional skill

Framework programmable platform for the advanced software development workstation. Integration mechanism design document

The Framework Programmable Software Development Platform (FPP) is a project aimed at combining effective tool and data integration mechanisms with a model of the software development process in an intelligent integrated software development environment. Guided by this model, this system development framework will take advantage of an integrated operating environment to automate effectively the management of the software development process so that costly mistakes during the development phase can be eliminated

Framework Programmable Platform for the advanced software development workstation: Framework processor design document

The design of the Framework Processor (FP) component of the Framework Programmable Software Development Platform (FFP) is described. The FFP is a project aimed at combining effective tool and data integration mechanisms with a model of the software development process in an intelligent integrated software development environment. Guided by the model, this Framework Processor will take advantage of an integrated operating environment to provide automated support for the management and control of the software development process so that costly mistakes during the development phase can be eliminated

A new insight into the observation of spectroscopic strength reduction in atomic nuclei: implication for the physical meaning of spectroscopic factors

Experimental studies of one nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a non-standard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon (NN) interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The method also reproduces the recently established relation between reduction of spectroscopic strength, observed in knockout reactions on other nuclei, and nucleon binding energies. The implication of the inhomogeneous equation method for the physical meaning of spectroscopic factors is discussed.Comment: 4 pages, accepted by Phys. Rev. Let

Primordial Earth mantle heterogeneity caused by the Moon-forming giant impact

The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally similar to the disk, out of which the Moon evolves, whereas the lower layer preserves proto-Earth characteristics. As long as this predicted compositional stratification can at least partially be preserved over the subsequent billions of years of Earth mantle convection, the compositional similarity between the Moon and the accessible Earth's mantle is a natural outcome of realistic and high-probability Moon-forming impact scenarios. The preservation of primordial heterogeneity in the modern Earth not only reconciles geochemical constraints but is also consistent with recent geophysical observations. Furthermore, for significant preservation of a proto-Earth reservoir, the bulk composition of the Earth-Moon system may be systematically shifted towards chondritic values.Comment: Comments are welcom

On the spectrum of Farey and Gauss maps

In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced version, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic properties of the associated dynamical zeta functions.Comment: 23 page