A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Vulnerability, scar, or reciprocal risk? Temporal ordering of self-esteem and depressive symptoms over 25 years

Three models have been proposed to explain the temporal interrelation between self-esteem and symptoms of depression: vulnerability (self-esteem predicts future depressive symptoms), scar (depressive symptoms predict future self-esteem), and reciprocal risk (self-esteem and depressive symptoms predict each other in the future). This study tested these three models over 25 years in a sample of high school seniors surveyed six times from age 18 to 43 (n = 978) and in a separate sample of university graduates surveyed five times from age 23 to 30 (n = 589). In both samples, autoregressive cross-lagged modeling results were that self-esteem and symptoms of depression prospectively predicted each other at every measurement occasion. Additionally, the cross-lagged association from self-esteem to symptoms of depression and the corresponding link from depressive symptoms to future self-esteem were equally strong. These results provide support for the reciprocal risk model

Paths to success in young adulthood from mental health and life transitions in emerging adulthood

This study followed a school-based sample (N = 920) to explore how trajectories of depressive symptoms and expressed anger from age 18 to 25, along with important life transitions, predicted life and career satisfaction at age 32. A two-group (women and men) bivariate growth model revealed that higher depressive symptoms at age 18 predicted lower life satisfaction in men and women, and lower career satisfaction in women. Slower declines across emerging adulthood in women's depressive symptoms predicted lower life satisfaction, but slower declines in women's expressed anger predicted higher career satisfaction. Marital and employment-related transitions were differentially related to men's and women's life and career satisfaction. Paths to success in young adulthood are diverse and gendered

Exploring or Floundering? The Meaning of Employment and Educational Fluctuations in Emerging Adulthood

Youth today spend years moving in and out of different education and employment statuses until they settle into stable employment. This 14-year Canadian longitudinal study reveals how month-to-month fluctuations in employment and educational statuses from age 19 to 25 predict employment success at age 32. Early employment instability was linked to lower income at age 32 and, among men, to lower occupational status and career satisfaction. However, for those who had made at least one career change, employment fluctuation had a positive effect on income and career satisfaction. Greater fluctuation in educational status was associated with higher occupational status at age 32. In general, labor market instability in the early 20smight best be described as floundering, while educational status changes more often reflect exploring

Forecasting life and career satisfaction in midlife from young adult depressive symptoms

This 14-year, six-wave longitudinal study of 583 university graduates examined whether trajectories of depressive symptoms from age 23 to 30 predicted life and career satisfaction outcomes at age 37, after controlling for (a) time-varying associations of marriage and unemployment with depressive symptoms, (b) sociodemographic characteristics (age, sex, parents' education), and (c) family and labor market experiences assessed at age 37 (marriage and divorce, raising children, income, spells of unemployment, occupational status). Net of the effects of all covariates, lower depressive symptoms at age 23 predicted higher life and career satisfaction at age 37, and steeper declines in depressive symptoms predicted higher life satisfaction. From age 23 to 30, being married was associated with fewer depressive symptoms, and more unemployment (in months) was associated with more depressive symptoms. The course of depressive symptoms through young adulthood carries over into midlife, showing continuity even after accounting for family and labor market experiences

Les politiques de négociation du gouvernement fédéral canadien, selon la loi et selon les décisions administratives

Numéro de référence interne originel : A1.328 WP 930