A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

The non-existence of a universal topological type space

The concept of types was introduced by Harsányi[8]. In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet [11] showed that the universal type space exists and later Meier[13] proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces.

Determinants of resource development strategies in nonprofit organizations: An analysis of children, youth and family services

This study is an exploratory analysis of an operational measure for resource development strategies, and an exploratory analysis of internal organizational contingencies influencing choices of these strategies in charitable nonprofit organizations. The study provides conceptual guidance for advancing understanding about resource development in the nonprofit sector. The statistical findings are, however, inconclusive without further rigorous examination. A three category typology based on organization technology is initially presented to define the strategies. Three dimensions of internal organizational contingencies explored represent organization identity, professional staff, and boards of directors. Based on relevant literature and key informant interviews, an original survey was administered by mail to a national sample of nonprofit organizations. The survey collected data on indicators of the proposed strategy types and selected contingencies. Factor analysis extracted two of the initial categories in the typology. The Building Resource Development Infrastructure Strategy encompasses information technology, personnel, legal structures, and policies facilitating fund development. The Building Resource Development Infrastructure Strategy encompasses the mission, service niche, and type of service delivery forming the basis for seeking financial support. Linear regressions with each strategy type as the dependent variable identified distinct and common contingencies which may partly explain choices of strategies. Discriminant analysis suggests the potential predictive accuracy of the contingencies. Follow-up case studies with survey respondents provide additional criteria for operationalizing future measures of resource development strategies, and support and expand the analysis on contingencies. The typology offers a beginning framework for defining alternative approaches to resource development, and for exploring organization capacity specific to each approach. Contingencies that may be integral components of organization capacity are funding, leadership frame, background and experience, staff and volunteer effort, board member support, and relationships in the external environment. Based on these findings, management questions are offered for nonprofit organization stakeholders to consider in planning for resource development. Lessons learned in designing and conducting this study are also provided to enhance future related research. ^

Teachers' experiences in and perceptions of their 12th-grade British literature classrooms

The purpose of this study was to understand the experiences and perceptions of 12th-grade literature teachers about curriculum, Post-Colonial literature, and students. Theories posed by Piaget (1995), Vygotsky (1995), and Rosenblatt (1995) formed the framework for this micro-ethnographic study. Seven teachers from public and private schools in South Florida participated in this two-phase study; three teachers in Phase I and four in Phase II. All participants completed individual semi-structured interviews and demographic surveys. In addition, four of the teachers were observed teaching. The analysis yielded three themes and two sub-themes: (a) knowledge concerned teachers' knowledge of British literature content and Post-Colonial authors and their literature; (b) freedom described teachers' freedom to choose how to teach their content. Included in this theme was dilemmas associated with 12th-grade classrooms which described issues that were pertinent to the 12th-grade teacher and classroom that were revealed by the study; and (c) thoughts about students described teachers' perceptions about students and how literature might affect the students. Two subthemes of knowledge were as follows:(1) text complexity described teacher responses to a Post-Colonial text's complexity and (2) student desirability/teachability described teachers' perception about how desirable Post-Colonial texts would be to students and whether teachers would be willing to teach these texts. The researcher offers recommendations for understanding factors associated with 12th-grade teachers perceptions and implications for enhancing the 12th-grade experience for teachers and curriculum, based on this study: (a) build teacher morale and capacity, (b) treat all students as integral components of the teaching and learning process; teachers in this study thought teaching disenfranchised learners was a form of punishment meted out by the administration, and (c) include more Post-Colonial authors in school curricula in colleges and schools as most teachers in this study did not study this type of literature nor knew how to teach it.

Observation of manganese nodules and manganese coated coral in the West Northern Atlantic ocean

Photography has become an integral part of submarine geological and biological investigations of the ocean bottom. The underwater cameras used to make these photographs were designed by Harold Edgerton. The pictures were taken from 1960 to 1962, from ships of the Woods Hole Oceanographic Institution. They show that life occurs even in the deepest trenches, and that sedimentary and biological processes in deep water do not differ in kind from those in shallow water.

The Rotational Evolution and Magnetospheric Emission of the Magnetic Early B-type Stars

How do the magnetic fields of massive stars evolve over time? Are their gyrochronological ages consistent with ages inferred from evolutionary tracks? Why do most stars predicted to host Centrifugal Magnetospheres (CMs) display no H$\alpha$ emission? Does plasma escape from CMs via centrifugal breakout events, or by a steady-state leakage mechanism? This thesis investigates these questions via a population study with a sample of 51 magnetic early B-type stars. The longitudinal magnetic field \bz~was measured from Least Squares Deconvolution profiles extracted from high-resolution spectropolarimetric data. New rotational periods $P_{\rm rot}$ were determined for 15 stars from \bz, leaving only 3 stars for which $P_{\rm rot}$ is unknown. Projected rotational velocities \vsini~were measured from multiple spectral lines. Effective temperatures and surface gravities were measured via ionization balances and line profile fitting of H Balmer lines. Fundamental physical parameters, \bz, \vsini, and $P_{\rm rot}$ were then used to determine radii, masses, ages, dipole oblique rotator model, stellar wind, magnetospheric, and spindown parameters using a Monte Carlo approach that self-consistently calculates all parameters while accounting for all available constraints on stellar properties. Dipole magnetic field strengths $B_{\rm d}$ follow a log-normal distribution similar to that of Ap stars, and decline over time in a fashion consistent with the expected conservation of fossil magnetic flux. $P_{\rm rot}$ increases with fractional main sequence age, mass, and $B_{\rm d}$, as expected from magnetospheric braking. However, comparison of evolutionary track ages to maximum spindown ages $t_{\rm S,max}$ shows that initial rotation fractions may be far below critical for stars with $M_*>10 M_\odot$. Computing $t_{\rm S,max}$ with different mass-loss prescriptions indicates that the mass-loss rates of B-type stars are likely much lower than expected from extrapolation from O-type stars. Stars with H$\alpha$ in emission and absorption occupy distinct regions in the updated rotation-magnetic confinement diagram: H$\alpha$-bright stars are found to be younger, more rapidly rotating, and more strongly magnetized than the general population. Emission strength is sensitive both to the volume of the CM and to the mass-loss rate, favouring leakage over centrifugal breakout.

Long-term statin therapy in patients with systolic heart failure and normal cholesterol:effects on elevated serum markers of collagen turnover, inflammation, and B-type natriuretic peptide

BACKGROUND: The role of statin therapy in heart failure (HF) is unclear. The amino-terminal propeptide of procollagen type III (PIIINP) predicts outcome in HF, and yet there are conflicting reports of statin therapy effects on PIIINP.

OBJECTIVES: This study determined whether there was an increase in serum markers of inflammation, fibrosis (including PIIINP), and B-type natriuretic peptide (BNP) in patients with systolic HF and normal total cholesterol and determined the effects of long-term treatment with atorvastatin on these markers.

METHODS: Fifty-six white patients with systolic HF and normal cholesterol levels (age 72 [13] years; 68% male; body mass index 27.0 [7.3] kg/m(2); ejection fraction 35 [13]%; 46% with history of smoking) were randomly allocated to atorvastatin treatment for 6 months, titrated to 40 mg/d (A group) or not (C group). Age- and/or sex-matched subjects without HF (N group) were also recruited. Biomarkers were measured at baseline (all groups) and 6 months (A and C groups).

RESULTS: Serum markers of collagen turnover, inflammation, and BNP were significantly elevated in HF patients compared with normal participants (all P < 0.05). There were correlations between these markers in HF patients but not in normal subjects. Atorvastatin treatment for 6 months caused a significant reduction in the following biomarkers compared with baseline: BNP, from median (interquartile range) 268 (190-441) pg/mL to 185 (144-344) pg/mL; high-sensitivity C-reactive protein (hs-CRP), from 5.26 (1.95 -9.29) mg/L to 3.70 (2.34-6.81) mg/L; and PIIINP, from 4.65 (1.86) to 4.09 (1.25) pg/mL (all P < 0.05 baseline vs 6 months). Between-group differences were significant for PIIINP only (P = 0.027). There was a positive interaction between atorvastatin effects and baseline hs-CRP and PIIINP (P < 0.01).

CONCLUSIONS: Long-term statin therapy reduced PIIINP in this small, selected HF population with elevated baseline levels. Further evaluation of statin therapy in the management of HF patients with elevated PIIINP is warranted.

The VLT-FLAMES Tarantula Survey: XIX. B-type supergiants: Atmospheric parameters and nitrogen abundances to investigate the role of binarity and the width of the main sequence

Context: Model atmosphere analyses have been previously undertaken for both Galactic and extragalactic B-type supergiants. By contrast, little attention has been given to a comparison of the properties of single supergiants and those that are members of multiple systems. 

Aims: Atmospheric parameters and nitrogen abundances have been estimated for all the B-type supergiants identified in the VLT-FLAMES Tarantula survey. These include both single targets and binary candidates. The results have been analysed to investigate the role of binarity in the evolutionary history of supergiants. 

Methods: tlusty non-local thermodynamic equilibrium (LTE) model atmosphere calculations have been used to determine atmospheric parameters and nitrogen abundances for 34 single and 18 binary supergiants. Effective temperatures were deduced using the silicon balance technique, complemented by the helium ionisation in the hotter spectra. Surface gravities were estimated using Balmer line profiles and microturbulent velocities deduced using the silicon spectrum. Nitrogen abundances or upper limits were estimated from the Nii spectrum. The effects of a flux contribution from an unseen secondary were considered for the binary sample. Results. We present the first systematic study of the incidence of binarity for a sample of B-type supergiants across the theoretical terminal age main sequence (TAMS). To account for the distribution of effective temperatures of the B-type supergiants it may be necessary to extend the TAMS to lower temperatures. This is also consistent with the derived distribution of mass discrepancies, projected rotational velocities and nitrogen abundances, provided that stars cooler than this temperature are post-red supergiant objects. For all the supergiants in the Tarantula and in a previous FLAMES survey, the majority have small projected rotational velocities. The distribution peaks at about 50 km s^-1 with 65% in the range 30 km s^-1 ≤ ν_e sin i ≤ 60 km s^-1. About ten per cent have larger ve sin i (≥100 km s^-1), but surprisingly these show little or no nitrogen enhancement. All the cooler supergiants have low projected rotational velocities of ≤70 km s^-1 and high nitrogen abundance estimates, implying that either bi-stability braking or evolution on a blue loop may be important. Additionally, there is a lack of cooler binaries, possibly reflecting the small sample sizes. Single-star evolutionary models, which include rotation, can account for all of the nitrogen enhancement in both the single and binary samples. The detailed distribution of nitrogen abundances in the single and binary samples may be different, possibly reflecting differences in their evolutionary history. 

Conclusions: The first comparative study of single and binary B-type supergiants has revealed that the main sequence may be significantly wider than previously assumed, extending to T_eff = 20 000 K. Some marginal differences in single and binary atmospheric parameters and abundances have been identified, possibly implying non-standard evolution for some of the sample. This sample as a whole has implications for several aspects of our understanding of the evolutionary status of blue supergiants.

Rotational velocities of single and binary O-type stars in the Tarantula Nebula

Rotation is a key parameter in the evolution of massive stars, affecting their evolution, chemical yields, ionizing photon budget, and final fate. We determined the projected rotational velocity, υ e sin i, of ~330 O-type objects, i.e. ~210 spectroscopic single stars and ~110 primaries in binary systems, in the Tarantula nebula or 30 Doradus (30 Dor) region. The observations were taken using VLT/FLAMES and constitute the largest homogeneous dataset of multi-epoch spectroscopy of O-type stars currently available. The most distinctive feature of the υ e sin i distributions of the presumed-single stars and primaries in 30 Dor is a low-velocity peak at around 100 km s^-1. Stellar winds are not expected to have spun-down the bulk of the stars significantly since their arrival on the main sequence and therefore the peak in the single star sample is likely to represent the outcome of the formation process. Whereas the spin distribution of presumed-single stars shows a well developed tail of stars rotating more rapidly than 300 km s^-1, the sample of primaries does not feature such a high-velocity tail. The tail of the presumed-single star distribution is attributed for the most part - and could potentially be completely due - to spun-up binary products that appear as single stars or that have merged. This would be consistent with the lack of such post-interaction products in the binary sample, that is expected to be dominated by pre-interaction systems. The peak in this distribution is broader and is shifted toward somewhat higher spin rates compared to the distribution of presumed-single stars. Systems displaying large radial velocity variations, typical for short period systems, appear mostly responsible for these differences.

The VLT-FLAMES tarantula survey:XII. Rotational velocities of the single O-type stars

Context. The 30 Doradus (30 Dor) region of the Large Magellanic Cloud, also known as the Tarantula nebula, is the nearest starburst region. It contains the richest population of massive stars in the Local Group, and it is thus the best possible laboratory to investigate open questions on the formation and evolution of massive stars. Aims. Using ground-based multi-object optical spectroscopy obtained in the framework of the VLT-FLAMES Tarantula Survey (VFTS), we aim to establish the (projected) rotational velocity distribution for a sample of 216 presumably single O-type stars in 30 Dor. The sample is large enough to obtain statistically significant information and to search for variations among subpopulations - in terms of spectral type, luminosity class, and spatial location - in the field of view. Methods. We measured projected rotational velocities, 3e sin i, by means of a Fourier transform method and a profile fitting method applied to a set of isolated spectral lines. We also used an iterative deconvolution procedure to infer the probability density, P(3e), of the equatorial rotational velocity, 3e. Results. The distribution of 3e sin i shows a two-component structure: a peak around 80 km s1 and a high-velocity tail extending up to 600 km s^-1 This structure is also present in the inferred distribution P(3e) with around 80% of the sample having 0 <3e ≤ 300 km s^-1 and the other 20% distributed in the high-velocity region. The presence of the low-velocity peak is consistent with what has been found in other studies for late O- and early B-type stars. Conclusions. Most of the stars in our sample rotate with a rate less than 20% of their break-up velocity. For the bulk of the sample, mass loss in a stellar wind and/or envelope expansion is not efficient enough to significantly spin down these stars within the first few Myr of evolution. If massive-star formation results in stars rotating at birth with a large portion of their break-up velocities, an alternative braking mechanism, possibly magnetic fields, is thus required to explain the present-day rotational properties of the O-type stars in 30 Dor. The presence of a sizeable population of fast rotators is compatible with recent population synthesis computations that investigate the influence of binary evolution on the rotation rate of massive stars. Even though we have excluded stars that show significant radial velocity variations, our sample may have remained contaminated by post-interaction binary products. That the highvelocity tail may be populated primarily (and perhaps exclusively) by post-binary interaction products has important implications for the evolutionary origin of systems that produce gamma-ray bursts. © 2013 Author(s).

Comparing long-term placements for young children in care: Does type of placement really matter?

This paper presents findings from the third phase of a longitudinal study, entitled Care Pathways and Outcomes, which has been tracking the placements and measuring outcomes for a population of children (n = 374) who were under the age of five and in care in Northern Ireland on the 31st March 2000. It explores how a sub-sample of these children at age nine to 14 years old were getting on in the placements provided for them, in comparative terms across five placement types: adoption; foster care; kinship foster care (with relatives); on Residence Order; and living with birth parents. This specifically focused on the development of attachment and self-concept from the perspective of the children, and behavioural and emotional function, and parenting stress, from the perspective of parents and carers. Findings showed no significant placement effect from the perspective of children, and a statistically weak, but descriptively compelling, effect from the perspective of parents. The findings challenge the notion of adoption as the gold standard in long-term placements, specifically from the perspective of children in terms of their parent/carer attachments and self-concept, and highlight what appears to be the central importance of placement longevity for delivering positive longer-term outcomes for these children, irrespective of placement type.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Predicting polarization signatures for double-detonation and delayed-detonation models of Type Ia supernovae

Calculations of synthetic spectropolarimetry are one means to test multidimensional explosion models for Type Ia supernovae. In a recent paper, we demonstrated that the violent merger of a 1.1 and 0.9 M⊙ white dwarf binary system is too asymmetric to explain the low polarization levels commonly observed in normal Type Ia supernovae. Here, we present polarization simulations for two alternative scenarios: the sub-Chandrasekhar mass double-detonation and the Chandrasekhar mass delayed-detonation model. Specifically, we study a 2D double-detonation model and a 3D delayed-detonation model, and calculate polarization spectra for multiple observer orientations in both cases. We find modest polarization levels (<1 per cent) for both explosion models. Polarization in the continuum peaks at ∼0.1–0.3 per cent and decreases after maximum light, in excellent agreement with spectropolarimetric data of normal Type Ia supernovae. Higher degrees of polarization are found across individual spectral lines. In particular, the synthetic Si II λ6355 profiles are polarized at levels that match remarkably well the values observed in normal Type Ia supernovae, while the low degrees of polarization predicted across the O I λ7774 region are consistent with the non-detection of this feature in current data. We conclude that our models can reproduce many of the characteristics of both flux and polarization spectra for well-studied Type Ia supernovae, such as SN 2001el and SN 2012fr. However, the two models considered here cannot account for the unusually high level of polarization observed in extreme cases such as SN 2004dt.